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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2844f0 | problem | aim-0df1011a6fa8a3c46e2c977b7e2844f0 | Non-linear Roth | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Let $P$ be any (non-linear) polynomial, $A\subset \mathbb{F}_p$ with $|A|>p^{0.99}$. Does there always exist distinct $x,y$ such that
$$x,y,y+P(x)-P(y)\in A?$$ | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e2844f0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
When $P(x)=2x$, this recovers Roth's Theorem on 3-APs. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Boris Bukh | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2844f0",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.047Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8d78ecae-18bb-4146-9fc8-6cf174f8a3c9","format_issues":null,"number":7954} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e28513d | problem | aim-0df1011a6fa8a3c46e2c977b7e28513d | Entropy proof of Sidorenko | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Define a proof system for graph homomorphism inequalities using entropy. | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/1/#0df1011a6fa8a3c46e2c977b7e28513d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
There is a proof system for graph homomorphism inequalities using flag algebras. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
For example, prove that "$H$ is Sidorenko" is not provable in this proof system, for $H=K_{5,5}\setminus C_{10}$.
Can all known cases of Sidorenko be entropized?
Can the proof that even girth ... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Yufei Zhao | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e28513d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.035Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e9224584-1991-412c-afb6-bece249cbeb2","format_issues":null,"number":7952} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e285564 | problem | aim-0df1011a6fa8a3c46e2c977b7e285564 | How badly can Sidorenko fail for hypergraphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Let $H$ be a 3-uniform, 3-partite hypergraph. Then any $n$-vertex 3-uniform hypergraph with $pn^3$ edges contains at least $p^{Ce(H)}n^{V(H)}$ copies of $H$. | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/3/#0df1011a6fa8a3c46e2c977b7e285564",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
If $H\subset K_{t,t,t}^{(3)}$ with $t=v(H)/3$, then the number of copies of $H$ is known to be at least $p^{(v(H)/3)^3}n^{v(H)}$.
For graphs, the bound $p^{e(H)+v(H)/2}n^{v(H)}$ is known. This m... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jacob Fox | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e285564",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.075Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"75aa4d9e-744f-445e-a32d-4566f1bf9ac9","format_issues":null,"number":7960} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e28649b | problem | aim-0df1011a6fa8a3c46e2c977b7e28649b | Expansion of non-Sidorenko graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Does there exist a non-Sidorenko (hyper)graph $H$ whose $r$-expansion is Sidorenko? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/3/#0df1011a6fa8a3c46e2c977b7e28649b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Given a $k$-graph $F$, define the $r$-expansion of $F$ to be the $r$-graph obtained by enlarging each $k$-edge of $F$ with a set of $r-k$ vertices of degree one. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
It is known that an expansion of a Sidorenko graph is Sidorenko.
It is known that $C_5$ and its 3-expansion are not Sidorenko. More generally, if the girth (length of the shortest loose cycle) o... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sam Spiro | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e28649b",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.079Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"207f86b9-fa09-476b-bc84-ebc1cfd68a06","format_issues":null,"number":7961} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e288ab2 | problem | aim-0df1011a6fa8a3c46e2c977b7e288ab2 | Roth with common difference $p-1$ | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | For all $C>0$ and sufficiently large $N$, if $A\subset [N]$ with $|A|\geq N/\log^C N$, then there exists $x$ and $p$ prime such that
$$x,x+p-1,x+2(p-1)\in A.$$ | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e288ab2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A hard result of Green says that if $|A|>N^{1-c}$, then we can find $x,x+p-1\in A$, so we don't reasonably expect to get power-saving bounds for the above conjecture.
A model problem is the foll... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mehtaab Sawhney | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e288ab2",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.051Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"96ad8fd5-041a-4f3f-9b44-5f494370a2b8","format_issues":null,"number":7955} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e289c5c | problem | aim-0df1011a6fa8a3c46e2c977b7e289c5c | Roth with constrained differences | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | For which $0\in D\subseteq \mathbb{F}_p$ is it true that any $A\subset \mathbb{F}_p^n$ avoiding
$$x,x+y,x+2y\in A\quad \text{with } y\in D^n\setminus\{0\}$$
has size $\leq C^n$ for some $C < p$? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e289c5c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Slice rank + "multilinear trick" implies the problem is true for $|D|>p/2$.
For $D=\{0,1,2\}$, it is known that we must have $|A|\leq p^n/(\log\log\log n)^c$.
When $|D|=2$, Hales-Jewett gives $... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Huy Pham | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e289c5c",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.056Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0dfa2976-b66f-4898-b457-44f1e7b20c60","format_issues":null,"number":7956} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e28c410 | problem | aim-0df1011a6fa8a3c46e2c977b7e28c410 | Equi-isoclinic subspaces | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Let $N_\alpha^k(d)$ be the maximum number of $k$-dimensional subspaces of $\mathbb{R}^d$, every pair of which is equi-isoclinic with angle $\alpha$. Then
(1) $N_{\alpha}^k(d)=O_{\alpha,k}(d)$.
(2) $N_{\alpha}^k(d)=O_{k}(d)+o_{\alpha,k}(d)$. | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/4/#0df1011a6fa8a3c46e2c977b7e28c410",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Given $k$-dimensional linear subspaces $U,V\leq \mathbb{R}^d$, we say that $U,V$ are equi-isoclinic with angle $\alpha$ if every unit vector in $U$ projects down onto $V$ a vector of length $\alpha$. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The case $k=1$ gives equiangular lines, which is known, using Ramsey Theory.
$k=2$ generalizes "complex equiangular lines". Conjecture 1 is known for complex equiangular lines. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Yufei Zhao | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e28c410",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.093Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"84d4ccf6-ac76-4ccc-900e-e8a3e6c98a47","format_issues":null,"number":7964} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e28d94d | problem | aim-0df1011a6fa8a3c46e2c977b7e28d94d | Inverse theorem for equilateral triangles on the sphere | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | If $f$ is 1-bounded and $|Tf|>\delta$, does $f$ correlate with a function that depends on $O_{\delta}(1)$ coordinates (with respect to some basis)? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e28d94d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Denote by $S^n\subset \mathbb{R}^{n+1}$ the unit sphere. For a function $f:S^n\to \mathbb{R}$, define the quantity
$$Tf:= \mathbb{E}_{x,y,z\in S^n,x+y+z=0} f(x)f(y)f(z).$$ | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This is motivated by the following conjecture: the largest subset of the sphere avoiding $x+y+z=0$ is a hemisphere.
Let $T_{\alpha}f=\mathbb{E}_{x,y\in S^n,\langle x,y\rangle=\alpha} f(x)f(y)$.... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dmitrii Zakharov | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e28d94d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.060Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2eb5732d-14d0-4cad-a936-049277a77d9f","format_issues":null,"number":7957} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e28f5d8 | problem | aim-0df1011a6fa8a3c46e2c977b7e28f5d8 | Easier arithmetic Kakeya | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Let $S\subset\mathbb{Z}^n$ be such that for all $(d_1,\ldots,d_r)\in ([N]^n)^r$, $S$ contains the GAP (for some translate $a_0$)
$$\{a_0+i_1d_1+\cdots +i_rd_r : i_1,\ldots,i_r\in \{0,1,\ldots,k-1\}\}.$$
Then $|S|\geq N^{c_kn+o_{k\to\infty}(1)}$. | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e28f5d8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The case $r=1$ is a version of arithmetic Kakeya, and is known with bound $N^{0.59n+o_k(1)}$.
There is an equivalent entropic formulation. Let $X,Y_1,\ldots,Y_r$ be $\mathbb{Z}$-valued random va... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Manik Dhar | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
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] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e28f5d8",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.064Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2d25bf19-3dcc-4b0f-b540-06fbfabf2396","format_issues":null,"number":7958} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e290eba | problem | aim-0df1011a6fa8a3c46e2c977b7e290eba | Distinct distances and related problems | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | (1) Let $S\subset\mathbb{R}^2$ with no three points collinear. Then $S$ determines at least $|S|/2$ distinct distances.
(2) Given $n$ points in $\mathbb{R}^2$ with no three collinear. Then one can remove $O(1)$-many points so that the number of isosceles triangles is at most $1.99\binom{n}{2}$.
(3) Given a set $S$ of... | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/4/#0df1011a6fa8a3c46e2c977b7e290eba",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
(1) is known with $|S|/3$ distinct distances, by double counting isosceles triangles. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Cosmin Pohoata | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/4/",
"note": null,
"sort_order": 0
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] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e290eba",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.097Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"32ea20b7-7297-4f7a-aa00-665a3326e31b","format_issues":null,"number":7965} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2911f2 | problem | aim-0df1011a6fa8a3c46e2c977b7e2911f2 | Inverse theorems with polynomial bounds | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Is there a direct entropic proof of the above results with polynomial bounds? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/1/#0df1011a6fa8a3c46e2c977b7e2911f2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Given $f:\mathbb{F}_2^n\to \mathbb{F}_2^m$ with $\mathbb{P}_{x+y=z+w}(f(x)+f(y)=f(z)+f(w))\geq \epsilon$, then Polynomial Freiman-Ruzsa implies that $f$ correlates with a linear function.
Set $D_hf(x)=f(x+h)-f(x)$. If $\mathbb{P}_{x,h_1,h_2,h_3}(D_{h_1}D_{h_2}D_{h_3}f(x)=0)\geq \epsilon$, then PFR... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The second result is known with bounds $1/\exp(\exp(1/\epsilon))$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Freddie Manners | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2911f2",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.042Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4162e4c0-22dc-49ed-a2ab-60fef5ede657","format_issues":null,"number":7953} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e292f87 | problem | aim-0df1011a6fa8a3c46e2c977b7e292f87 | Induced packing and covering | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Can we get better bounds, even for the case $H=C_5$? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/3/#0df1011a6fa8a3c46e2c977b7e292f87",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Let $H$ be a fixed graph, $G$ an $n$-vertex graph. If the minimum number of edges needed to add or remove from $G$ in order to remove all induced copies of $H$ is $o(n^2)$, then the regularity lemma implies that the maximum number of induced copies of $H$, with each pair intersecting in at most one... | 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"
] | Jacob Fox | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e292f87",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.084Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48d81d9b-5ee6-4cac-b86a-9be9e3e6c2ed","format_issues":null,"number":7962} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2938e5 | problem | aim-0df1011a6fa8a3c46e2c977b7e2938e5 | Turan exponents of hypergraphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | There exists $c>0$ such that the following holds. If $H$ is an $n$-vertex, 3-uniform hypergraph with at least $n^{3-c/d}$ edges, then $H$ contains some/every 3-uniform, 3-partite linear hypergraph on $d$ vertices with at least $d^2/100$ edges. | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/3/#0df1011a6fa8a3c46e2c977b7e2938e5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
It is known that if $H$ has $\geq n^{3-c/d^2}$ edges, then it contains $K_{d,d,d}^{(3)}$.
Interesting cases are when $H$ is the set of triangles in some graph $G$, or a $p$-random subset of tria... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jonathan Tidor | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2938e5",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.088Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3f61ce11-5c8f-422a-a9f9-1fc324da45c0","format_issues":null,"number":7963} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e293c5d | problem | aim-0df1011a6fa8a3c46e2c977b7e293c5d | Popular Furstenberg–Sárközy | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | (1) Prove lower bounds of the form $N_0(\epsilon)>superpoly(1/\epsilon)$, or even just $N_0(\epsilon)>1/\epsilon^{10}$.
(2) What happens in the function field case $\mathbb{F}_p[t]_{< n}$? Can we prove upper/lower bounds? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/2/#0df1011a6fa8a3c46e2c977b7e293c5d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
(Furstenberg–Sárközy) For all $\epsilon>0$, there exists $N_0=N_0(\epsilon)$ such that for all $N\geq N_0$, $A\subseteq [N]$ with $|A|\geq \delta N$, there exists $y\neq 0$ such that
$$|\{x : x,x+y^2\in A\}|\geq (\delta^2-\epsilon)N,$$
with $N_0(\epsilon)\leq e^{1/\epsilon^c}$. | 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"
] | Sean Prendiville | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e293c5d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.069Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b852aff4-3d0e-40a1-b6aa-fe618a2917ed","format_issues":null,"number":7959} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e29430e | problem | aim-0df1011a6fa8a3c46e2c977b7e29430e | Kupitz conjecture in three dimensions | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Given $n$ points in $\mathbb{R}^3$, is there always a plane through at least two points, such that the number of points on each side differ by $O(1)$? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/4/#0df1011a6fa8a3c46e2c977b7e29430e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
(Kupitz conjecture) Given $n$ points in $\mathbb{R}^2$, is there always a line through at least two points, such that the number of points on each side differ by $O(1)$? | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
For Kupitz conjecture, if the optimal bound is $C$, then it is known that $2\leq C\leq O(\log\log n)$. For pseudoline arrangements, $C=\Theta(\log\log n)$.
For 3D, the same upper bound $O(\log\l... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jeck Lim | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e29430e",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.101Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fe72db7a-c8c3-44a0-be15-3e08e2cb6304","format_issues":null,"number":7966} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2a368c | problem | aim-0df1011a6fa8a3c46e2c977b7e2a368c | Analogous of paths on iterated monodromy groups for iterated Galois groups of dynamical maps | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | 1. Can we algebraically construct "nice" paths to describe $G_\infty^{geom}$ by more explicit wreath recursions? More precisely, given $z\in f^{-1}(t)$, can we find explicit endomorphisms of $K_\infty$, perhaps recursively described, sending $t$ to $z$ with nice properties? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/1/#0df1011a6fa8a3c46e2c977b7e2a368c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $k$ be a field, $f \in k(z)$ of degree at least $2$, and $t$ be a transcendental number. Define $k_\infty = k \left( \cup_{n \geq 0} f^{-n}(t) \right)$, $L = k_\infty \cap \overline{k}$, $G_\infty = Gal(k_\infty/k(t))$ and $G_\infty^{geom} = Gal(k_\infty/L(t))$. \\
It was proved by Richard Pin... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Presently, we can only get wreath recursions up to conjugacy by algebraic methods, and Pink shows that for quadratic PCF polynomials these choices do not matter. We cannot expect to easily obtai... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ophelia Adams | null | null | null | [
{
"kind": "website",
"citation": "Groups of dynamical origin",
"url": "http://aimpl.org/groupdynamorigin/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2a368c",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:10.650Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"45553307-ae3e-4e48-8b8c-a79855a7fc0f","format_issues":null,"number":7654} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2a4df6 | problem | aim-0df1011a6fa8a3c46e2c977b7e2a4df6 | Orbit equivalence for IMG | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | 1. Can we find $\varphi \in Homeo(\partial T)$ such that the orbit of the group generated by $\varphi$ and $IMG(f)$ are orbit equivalent?
2. Can we make $\varphi$ explicit? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/1/#0df1011a6fa8a3c46e2c977b7e2a4df6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $G,H$ two groups acting on the same set $X$. We say that $G$ and $H$ are **orbit equivalent** if they have the same orbits. \\
Let $f$ be a continuous map and $IMG(f)$ its iterated monodromy group. Assume $IMG(f)$ is countable and consider its action on $\partial T$, the boundary of the tree. ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A result in this direction is \cite{MR2563761} where it is proved $\rho$ is an action of $\mathbb{Z}^d$ over a Cantor set that is free and minimal, then $\rho$ is orbit equivalent to an action of... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Constantine Medynets | null | null | null | [
{
"kind": "website",
"citation": "Groups of dynamical origin",
"url": "http://aimpl.org/groupdynamorigin/1/",
"note": null,
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2a61f7 | problem | aim-0df1011a6fa8a3c46e2c977b7e2a61f7 | Groups of subshifts not containing consecutive letters | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - Describe relations in $G_\mathcal{F}$.
- Can $\mathcal{H}_\mathcal{F}$ be algebraically interpreted as an invariant inside $G_\mathcal{F}$?
- What is \textcolor{red}{in between (need explanation here)} minimal $S_\mathcal{F}$ and shifts of finite type?
- If $\mathcal{H}_\mathcal{F} = 0$, does eith... | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/groupdynamorigin/2/#0df1011a6fa8a3c46e2c977b7e2a61f7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $A$ be a finite alphabet, $A^*$ the set of finite words in $A$ and $\mathcal{F} \subseteq A^*$ a set of forbidden patterns that contains the set $\left\{aa: a \in A\right\}$. Let $$S_\mathcal{F} = \left\{x \in A^\mathbb{Z}: \text{ $x$ contains no subword in $\mathcal{F}$}\right\}.$$
Define $\v... | 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"
] | Constantine Medynets | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2a74b7 | problem | aim-0df1011a6fa8a3c46e2c977b7e2a74b7 | Defining relations for subgroups of full group of a shift | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is it true that for all finitely generated subgroup $H \leq F(\Omega)$, $H$ is either elementary amenable or for any $K$ finitely presented subgroup such that $K \twoheadrightarrow H$, $K$ contains a free subgroup? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/2/#0df1011a6fa8a3c46e2c977b7e2a74b7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $A$ be a finite alphabet and $\Omega$ be a 2-sided subshift, i.e., a closed subset of $A^\mathbb{Z}$ that is invariant under the shift map $\sigma$. An element $g \in Homeo(\Omega)$ belong to the full group of the shift ($F(\Omega)$) if each point in $\Omega$ has an open neighborhood $U$ such t... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Two inspiring results come from \cite{MR3061134}, \cite{MR3395261} and \cite{arXiv:2304.11232}:
- There exists $G$ such that the Grigorchuk group embeds as a subgroup of $G$ but the Grig... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Volodymyr Nekrashevych | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2a947e | problem | aim-0df1011a6fa8a3c46e2c977b7e2a947e | Entropy of subshifts of finite type | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - Given a recursively presented and finitely generated infinite amenable group $G$, what is $E_G$?
- Does there exist a recursively presented and finitely generated infinite amenable group $G$ such that $E_\mathbb{Z} \subsetneq E_G \subsetneq E_{\mathbb{Z}^2}$? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
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"url": "http://aimpl.org/groupdynamorigin/2/#0df1011a6fa8a3c46e2c977b7e2a947e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $G$ be a finitely generated infinite ameanable group, $A$ be a finite alphabet and define $$\mathcal{F} = \left\{f:B \rightarrow A: B \subseteq G \text{ finite}\right\}$$ a finite set of forbidden patterns and $$S_{G,\mathcal{F}, A} = \left\{x \in A^G: x \text{ contains no forbidden subpatterns... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Results known: if $G$ is a finitely generated branch, torsion-free group with solvable word problem, then $E_G = E_{\mathbb{Z}^2}$. See \cite{MR4303334}. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sebastian Barbieri | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2aa289 | problem | aim-0df1011a6fa8a3c46e2c977b7e2aa289 | Growths functions of repetitive graphs | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What functions can be realized as growths functions of repetitive graphs? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/4/#0df1011a6fa8a3c46e2c977b7e2aa289",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
A graph $\Gamma$ is called **repetitive** if for all $r > 0$ there exists $d > 0$ such that for all $x,y \in \Gamma$, there exists an isomorphic copy of $B_r(x)$ (the ball of radius $r$ centered at $x$) at distance less or equal to $d$ from $y$. \\
Consider two kind of growths functions for $\Gamm... | 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"
] | Nicolas Matte Bon | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2ab003 | problem | aim-0df1011a6fa8a3c46e2c977b7e2ab003 | Nekrashevych C-algebras | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | When is the Nekrashevych $C^*$-algebra of a contracting group simple? | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/4/#0df1011a6fa8a3c46e2c977b7e2ab003",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · 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-0df1011a6fa8a3c46e2c977b7e2abc80 | problem | aim-0df1011a6fa8a3c46e2c977b7e2abc80 | Properties of subgroups of topological full groups | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Try to understand relations, amenability and Liouville property of subgroups of topological full groups. In particular of $\left\langle \delta_a: a \in A \right\rangle$ | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
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"url": "http://aimpl.org/groupdynamorigin/2/#0df1011a6fa8a3c46e2c977b7e2abc80",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · 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-0df1011a6fa8a3c46e2c977b7e2ad419 | problem | aim-0df1011a6fa8a3c46e2c977b7e2ad419 | Wreath recursion for Galois groups | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | 1. Contruct explicit wreath recursions for Galois groups
2. Under what conditions is a group coming from a Galois arboreal representation a branch group? | unassessed | {
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"license": "Editorially moderated; per-list terms",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2af3c4 | problem | aim-0df1011a6fa8a3c46e2c977b7e2af3c4 | Commutator width of Thompson groups | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - Prove that $\rho_1$ and $\rho_2$ are bounded
- Prove that $\rho_1 = 1$ and $\rho_2 = 3$
- Is there a finitely presented simple group with commutator width greater or equal to $2$? | unassessed | {
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"url": "http://aimpl.org/groupdynamorigin/3/#0df1011a6fa8a3c46e2c977b7e2af3c4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $G$ be $F,T$ or $V$ or a topological full group. Let $\rho_1(g)$ be the commutator width of $g$ and $\rho_2(g)$ the minimum number of involutions in a factorization of $g$. | 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-0df1011a6fa8a3c46e2c977b7e2afdb3 | problem | aim-0df1011a6fa8a3c46e2c977b7e2afdb3 | Maximal subgroups in Thompson groups | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Find new maximal subgroups of infinite index in Thompson groups | unassessed | {
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"url": "http://aimpl.org/groupdynamorigin/3/#0df1011a6fa8a3c46e2c977b7e2afdb3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · 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-0df1011a6fa8a3c46e2c977b7e2b0aaa | problem | aim-0df1011a6fa8a3c46e2c977b7e2b0aaa | Fixed point proportion of dynamical exceptional polynomials | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | 1. What can we say about the fixed-point proportion of groups acting on rooted trees?
2. Fixing the tree $T$, can we find a family of groups such that its fixed-point proportion is nonzero and its Hausdorff dimension converges to $1$?
3. What can we say about the fixed-point proportion of Galois groups?
4. What can ... | unassessed | {
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"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $G$ be a group acting on a infinite rooted tree, and denote $G_n$ the action of $G$ on the first $n$ levels of the tree. We define the **fixed-point proportion** of $G$ as $$FPP(G) = \lim_{n \rightarrow +\infty} \frac{\# \left\{g \in G_n: \text{ $g$ fixes at least one element on level $n$}\righ... | 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"
] | Santiago Radi | null | null | null | [
{
"kind": "website",
"citation": "Groups of dynamical origin",
"url": "http://aimpl.org/groupdynamorigin/1/",
"note": null,
"sort_order": 0
}
] | {
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"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": "2026-09-08T03:33:10.664Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2d0bc849-9d1e-42f6-a352-a9b34911576b","format_issues":null,"number":7657} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2b4cd0 | problem | aim-0df1011a6fa8a3c46e2c977b7e2b4cd0 | Reconstructing the Julia set of a function from the iterated Galois group | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Can we reconstruct the $p$-adic Julia set of $f$ from $G_\infty$ or $G_\infty^{geom}$ | unassessed | {
"key": "aimpl",
"name": "AIM · Groups of dynamical origin",
"type": "workshop-problem-list",
"url": "http://aimpl.org/groupdynamorigin/1/#0df1011a6fa8a3c46e2c977b7e2b4cd0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Groups of dynamical origin · Historical workshop question | ## Question context
Let $k$ be a finite field extension of $\mathbb{Q}_p$, $f \in k(z)$ of degree at least $2$, and $t$ be a transcendental number. Define $k_\infty = k \left( \cup_{n \geq 0} f^{-n}(t) \right)$, $L = k_\infty \cap \overline{k}$, $G_\infty = Gal(k_\infty/k(t))$ and $G_\infty^{geom} = Gal(k_\infty/L(t))... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ophelia Adams | null | null | null | [
{
"kind": "website",
"citation": "Groups of dynamical origin",
"url": "http://aimpl.org/groupdynamorigin/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2b4cd0",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:10.670Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8234e1f3-5397-4535-b998-8cc9f781a2fd","format_issues":null,"number":7658} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2b9698 | problem | aim-0df1011a6fa8a3c46e2c977b7e2b9698 | $L^1$ norm of first eigenfunction. | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega\subset \mathbb{R}^n$ be an open set with finite measure, $\lambda_1(\Omega)$ be the first eigenvalue of the Laplacian with Dirichlet boundary conditions, and let
$$
T(\Omega)=\int_{\Omega}u
$$
where $u:\Omega\to \mathbb{R}$ is the torsion function given by the equation
$$
\begin{cases}
-\Delta u=1 & \tex... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/1/#0df1011a6fa8a3c46e2c977b7e2b9698",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Open questions about the shape and properties of ground states and torsion functions. | 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"
] | Phanuel Mariano | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2b9698",
"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": "2026-09-08T03:33:14.008Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"09f2e7b9-e2a3-48d9-bdd6-3978beaaaadc","format_issues":null,"number":8383} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2bb1fb | problem | aim-0df1011a6fa8a3c46e2c977b7e2bb1fb | Curl-curl eigenvalue problem | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega$ be a smooth compact domain of $\mathbb{R}^3$, we define $(\vec{E_k},\lambda_k)_{k\geq 1}$ to be the eigenpair of the Maxwell equation in $\Omega$, as given by the equation
\begin{align*}
\nabla \times \nabla \times \vec{E}_k & = \lambda_k \vec{E}_k \quad \text{in $\Omega$} \\
\nabla \cdot \vec{E}_k & = 0... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/2/#0df1011a6fa8a3c46e2c977b7e2bb1fb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions about the optimization of eigenvalues of several operator, under geometric constraints. | 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"
] | Nilima Nigam | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2bb1fb",
"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": "2026-09-08T03:33:14.025Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6419dcd5-48f5-4486-ad1e-dc10817f76d1","format_issues":null,"number":8386} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2bc143 | problem | aim-0df1011a6fa8a3c46e2c977b7e2bc143 | Curl eigenvalue | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega \subset \mathbb{R}^3$ be a bounded Lipschitz set with volume $1$, consider the curl eigenvalue problem
%
\begin{align*}
\nabla \times \vec{u} & = \mu \vec{u} \ \text{ on $\Omega$,} \\
\vec{\nu} \cdot \vec{u} & = 0 \ \text{ on $\partial \Omega$}.\\
\int_{\Omega}\vec u\cdot \vec w&=0 \ \text{ for any }\vec ... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/2/#0df1011a6fa8a3c46e2c977b7e2bc143",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions about the optimization of eigenvalues of several operator, under geometric constraints. | 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"
] | Iosif Polterovich | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2bc143",
"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": "2026-09-08T03:33:14.030Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0cf9c609-14db-4798-b582-ddfe4e2a93fc","format_issues":null,"number":8387} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2bca22 | problem | aim-0df1011a6fa8a3c46e2c977b7e2bca22 | Exterior Robin problem | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $n \geq 3$ and let $\Omega\subset\mathbb{R}^3$ be a smooth compact domain. For a given $\alpha \in \mathbb{R}$, we consider the Robin eigenvalue problem on the complement of $\Omega$, of unknown $(\lambda,u)$:
%
\begin{align*}
- \Delta u & = \lambda u \qquad \text{in $\Omega^\text{ext} = \mathbb{R}^n \setminus \ove... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/2/#0df1011a6fa8a3c46e2c977b7e2bca22",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions about the optimization of eigenvalues of several operator, under geometric constraints. | 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"
] | Lukas Bundrock | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2bca22",
"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": "2026-09-08T03:33:14.035Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3b7bca39-82b7-4af8-9bb4-287b2225d416","format_issues":null,"number":8388} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2bdb04 | problem | aim-0df1011a6fa8a3c46e2c977b7e2bdb04 | Maximizing Steklov $\sigma_1$ on $N$-gons | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | One of the ``well-known'' conjecture of shape optimization is the optimization of $\lambda_1$ (first eigenvalue of the Laplacian with Dirichlet boundary condition) among polygonal sets of fixed measure. A question raised by Iosif Polterovich on which even less is known is for the Steklov eigenvalue: given some integer ... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/2/#0df1011a6fa8a3c46e2c977b7e2bdb04",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions about the optimization of eigenvalues of several operator, under geometric constraints. | 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"
] | Iosif Polterovich | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2bdb04",
"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": "2026-09-08T03:33:14.040Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4f1a658c-1190-45bf-aeec-990e96c694bb","format_issues":null,"number":8389} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2be779 | problem | aim-0df1011a6fa8a3c46e2c977b7e2be779 | Maximal gradient of the torsion | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | This is a report of a question that was raised in (Hoskins, Steinerberger - 2021), and the following statement is based on this paper.
Let $\Omega \subset \mathbb{R}^2$ be a convex set, and $u_\Omega:\Omega\to \mathbb{R}$ be the torsion function defined by
%
\begin{align*}
- \Delta u_\Omega = 1 , & \qquad \text{in $\O... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/1/#0df1011a6fa8a3c46e2c977b7e2be779",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Open questions about the shape and properties of ground states and torsion functions. | 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"
] | Krzysztof Burdzy | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2be779",
"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": "2026-09-08T03:33:14.014Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"081a4a0c-c473-4cd3-a736-de83e718e30e","format_issues":null,"number":8384} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2bf55a | problem | aim-0df1011a6fa8a3c46e2c977b7e2bf55a | Shape of the ground state | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega\subset\mathbb{R}^n$ be a bounded convex set, and let $u$ be the lowest eigenfunction (ground state) of the Laplacian with Dirichet boundary conditions, with unit $L^2$ norm. A general question is to relate the domain $\Omega$ and the ground state $u$ with a rectangular domain $R$ associated to a ground stat... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/1/#0df1011a6fa8a3c46e2c977b7e2bf55a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Open questions about the shape and properties of ground states and torsion functions. | 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"
] | David Jerison | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2bf55a",
"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": "2026-09-08T03:33:14.020Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2ff5f3b6-fe93-408f-a796-72a152133177","format_issues":null,"number":8385} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c1107 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c1107 | Cheeger's inequality on convex sets | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For an open set of finite measure $\Omega\subset\mathbb{R}^n$, denote $\lambda_1(\Omega)$ the first eigenvalue of the Laplacian with Dirichlet boundary conditions, and $h(\Omega)$ the Cheeger constant which may be defined as
$$
h(\Omega)=\inf_{A\subset \Omega}\frac{|\partial A|}{|A|}=\inf_{u\in\mathcal{C}^\infty_c(\Om... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/3/#0df1011a6fa8a3c46e2c977b7e2c1107",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions involving geometric quantities such as isoperimetric profile, moment of inertia, rearrangements. | 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"
] | Ilias Ftouhi | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2c1107",
"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"
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c8c4f00a-ba75-4571-8734-051063e38d73","format_issues":null,"number":8391} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c1943 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c1943 | Slicing problem in 3 dimensions | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\Omega \subset \mathbb{R}^3$ is convex, normalized to have volume $1$, and with its center of mass at the origin. Let
$$
A_{ij} = \int_\Omega x_i x_j \, dx .
$$
The ball minimizes $\det A$. The problem is to find the shape that maximizes $\det A$.
This functional is affine invariant under linear maps wi... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/3/#0df1011a6fa8a3c46e2c977b7e2c1943",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions involving geometric quantities such as isoperimetric profile, moment of inertia, rearrangements. | 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"
] | Luis Rademacher | null | null | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d4fae564-950e-40ae-8ec4-2ca2c8c141b5","format_issues":null,"number":8392} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c1e4d | problem | aim-0df1011a6fa8a3c46e2c977b7e2c1e4d | Minimization of $p$-capacity | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $p\in (1,2)$, and $\Omega\subset \mathbb{R}^2$ a bounded convex set, we define its $p$-capacity
$$
\text{cap}_p(\Omega)=\inf\left\{\int_{\mathbb{R}^2}|\nabla u|^p,\ u\in\mathcal{C}^1_c(\mathbb{R}^2),\text{ such that }u\geq 1\text{ in a neighbourhood of }\Omega\right\}
$$
Note that this notion of capacity is not... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/2/#0df1011a6fa8a3c46e2c977b7e2c1e4d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions about the optimization of eigenvalues of several operator, under geometric constraints. | 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"
] | Dorin Bucur | null | null | null | [
{
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"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/2/",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
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] | [] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"55c04ace-ae44-46f8-8a4a-0eeb9a9fe903","format_issues":null,"number":8390} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c32b8 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c32b8 | Rearrangement problem | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Let $F:\mathbb{R}\to\mathbb{R}$ be an even convex function, then it is known (from Xi, Zhao (2022)) that for any function $f,g\in L^1(\mathbb{R}^n)$ (for some $n\geq 1$), denoting $f^*,g^*$ the symmetrically decreasing rearrangement of $f,g$, we have
$$
\iint_{R^n\times\mathbb{R}^n}F(x\cdot y)f(x)g(y)dxdy\geq \iint_{R... | unassessed | {
"key": "aimpl",
"name": "AIM · Symmetry-breaking of optimal shapes",
"type": "workshop-problem-list",
"url": "http://aimpl.org/symmetrybreaking/3/#0df1011a6fa8a3c46e2c977b7e2c32b8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Symmetry-breaking of optimal shapes · Historical workshop question | ## Section context
Questions involving geometric quantities such as isoperimetric profile, moment of inertia, rearrangements. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Paul Simanjuntak | null | null | null | [
{
"kind": "website",
"citation": "Symmetry-breaking of optimal shapes",
"url": "http://aimpl.org/symmetrybreaking/3/",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"7dec521a-abf3-4409-8045-cec0a244274d","format_issues":null,"number":8393} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c66a9 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c66a9 | Scissors Congruence · Question 1.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Consider the sequence
$$0\to \mathcal{P}(E^2) \xrightarrow{prism} \mathcal{P}(E^3)\to \mathbb{R}\otimes \mathbb{R}/\mathbb{Z} \to \Omega^1 \mathbb{R}/\mathbb{Z}\to 0,$$
which is known to be exact. There are two known proofs: one uses homological methods (Dupont), the other uses more elementary methods (Jessen). How do... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2c66a9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2c66a9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2b963a24-b5dd-4101-adb8-b30edab27aa8","format_issues":null,"number":11508} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c7d94 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c7d94 | Steinberg Modules & Homology · Question 3.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What can we say about $H_\ast(O(3)^\delta$)? $H_\ast(PSL_2(\mathbb{R})^\delta)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/3/#0df1011a6fa8a3c46e2c977b7e2c7d94",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/3/#0df1011a6fa8a3c46e2c977b7e2c7d94",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2c7d94",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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"created_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ae23d918-a763-4006-ab35-3db5bfe0323e","format_issues":null,"number":11516} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2c9113 | problem | aim-0df1011a6fa8a3c46e2c977b7e2c9113 | Scissors Congruence · Question 1.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is the map from Goncahrov's projectivised scissors congruence groups to the Hopf algebra of polylogarithms surjective? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2c9113",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2c9113",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ccfee69a-d7a0-4460-aa29-9671701a9a48","format_issues":null,"number":11509} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2cb143 | problem | aim-0df1011a6fa8a3c46e2c977b7e2cb143 | $K$-Theory and Algebraic Topology · Question 2.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a direct scanning map proof that scissors congruence $K$-theory of polytopes is a Thom spectrum? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2cb143",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2cb143",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.906Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"865552cd-e670-4aa4-b6ad-1c1bdf420274","format_issues":null,"number":11511} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2cc266 | problem | aim-0df1011a6fa8a3c46e2c977b7e2cc266 | $K$-Theory and Algebraic Topology · Question 2.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a $K$-theory spectrum that has homology groups $H_i(SL_n(\mathbb{Z});St(\mathbb{Q}))$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2cc266",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2cc266",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.911Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e2724aad-218b-4d65-8c47-fa010c597607","format_issues":null,"number":11512} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2cd0b2 | problem | aim-0df1011a6fa8a3c46e2c977b7e2cd0b2 | Scissors Congruence · Question 1.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | There are two different spectral sequences arising from Sah \& Goncharov; what is their relationship? Relation to the Minkowski Filtration? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2cd0b2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Scissors congruences, algebraic K-theory and Steinberg modules · Original question",
"url": "http://aimpl.org/scissorssteinberg/1/#0df1011a6fa8a3c46e2c977b7e2cd0b2",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"cc8aa521-84a4-4ba7-89bc-e60a13885f2a","format_issues":null,"number":11510} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2cd9d2 | problem | aim-0df1011a6fa8a3c46e2c977b7e2cd9d2 | $K$-Theory and Algebraic Topology · Question 2.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Develop projectivised scissors congruence $K$-theory. (For instance, can you prove polytopes with only vertices on the quadric generate the group?) | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2ceef3 | problem | aim-0df1011a6fa8a3c46e2c977b7e2ceef3 | $K$-Theory and Algebraic Topology · Question 2.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Develop universal characterisation for $K$-theory for the following kinds of categories:
- 1) Monoidal Categories
- 2) Exact Categories, CGW categories, Subtractive Categories
- 3) Multicategories
- 4) Squares | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2ceef3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · 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.
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"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2d0199 | problem | aim-0df1011a6fa8a3c46e2c977b7e2d0199 | $K$-Theory and Algebraic Topology · Question 2.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is the relationship between total scissors congruence \& discrete orthogonal $K$-Theory? Role of rank filtration of the associated $S_\bullet$-construction? | unassessed | {
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"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/2/#0df1011a6fa8a3c46e2c977b7e2d0199",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2d046a | problem | aim-0df1011a6fa8a3c46e2c977b7e2d046a | Steinberg Modules & Homology · Question 3.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Does $H_i(O(n)^\delta,St_n(\mathbb{R})\otimes \mathbb{Q})$ vanish for sufficiently large $n$? Applications to homological stability? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/3/#0df1011a6fa8a3c46e2c977b7e2d046a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"note": null,
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2d115f | problem | aim-0df1011a6fa8a3c46e2c977b7e2d115f | Steinberg Modules & Homology · Question 3.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Compute homology of $SK$-automorphism groups of manifolds. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Scissors congruences, algebraic K-theory and Steinberg modules",
"type": "workshop-problem-list",
"url": "http://aimpl.org/scissorssteinberg/3/#0df1011a6fa8a3c46e2c977b7e2d115f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Scissors congruences, algebraic K-theory and Steinberg modules · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"url": "http://aimpl.org/scissorssteinberg/3/#0df1011a6fa8a3c46e2c977b7e2d115f",
"note": null,
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2d54d7 | problem | aim-0df1011a6fa8a3c46e2c977b7e2d54d7 | EMT labeling of disjoint union of cycles | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | For even $n$, determine if the disjoint union $C_n \ \dot{\cup} \ C_n$ is edge-magic total. For $m \ge n$, determine if the disjoint union $C_m \ \dot{\cup} \ C_n$ is edge-magic total. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2d54d7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Bryan Freyberg | null | null | null | [
{
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"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2d54d7",
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"sort_order": 0
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2dcf57 | problem | aim-0df1011a6fa8a3c46e2c977b7e2dcf57 | Vertex distinguishing achromatic edge coloring | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Let $n \ge 4$. The maximum number of colors in a minimal vertex distinguishing edge labeling is $\lfloor \frac{2n}{3}\rfloor +1 $. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2dcf57",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Anne Saiko | null | null | null | [
{
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"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2dcf57",
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"sort_order": 0
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{
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"published_at": "2026-09-09T22:24:05.952Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8b5cc990-3686-4dd0-bfd6-8aafddc639b3","format_issues":null,"number":10844} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2e1df7 | problem | aim-0df1011a6fa8a3c46e2c977b7e2e1df7 | Radio graceful Cartesian graph products | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine conditions on graphs $G$ and $H$ that guarantee $G \ \square \ H$ is radio graceful. In the other direction, given $G \ \square \ H$ is radio graceful, determine if $G$ and $H$ are radio graceful. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2e1df7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Amanda Niedzialomski | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2e1df7",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e196ebc5-a119-4be1-9439-ca2754cf1b9a","format_issues":null,"number":10845} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2e306e | problem | aim-0df1011a6fa8a3c46e2c977b7e2e306e | EMT labeling for grid graphs | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Let $m \ge n$. Determine the validity of the existence of edge total labelings for $P_m \ \square \ P_n$. Determine the existence of edge total labelings for $C_m \ \square \ P_n$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2e306e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Bryan Freyberg | null | null | null | [
{
"kind": "website",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3bc58494-aacd-47b4-9496-b3c15819bf85","format_issues":null,"number":10846} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2e98d5 | problem | aim-0df1011a6fa8a3c46e2c977b7e2e98d5 | A linear algebra interpretation of labelings | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine linear algebra properties that correspond to the existence of particular labelings. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2e98d5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Veronika Furst | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2e98d5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2e98d5",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.970Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"83c8ad4a-425f-4e10-bd2a-be2e16b693ef","format_issues":null,"number":10847} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2eb0fc | problem | aim-0df1011a6fa8a3c46e2c977b7e2eb0fc | Variations on total labelings | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine which graphs admit such a graph labeling. For such graphs, determine the minimum number of labels required. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2eb0fc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Zhanar Berikkyzy | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2eb0fc",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2eb0fc",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.976Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7374cff5-f487-4572-b593-8e20834a39dc","format_issues":null,"number":10848} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2ebd9a | problem | aim-0df1011a6fa8a3c46e2c977b7e2ebd9a | Fractional labeling | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine graphs that admit such a fractional labeling. In particular, determine graphs that admit a fractional labeling but not an integer labeling. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2ebd9a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Aysel Erey | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2ebd9a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2ebd9a",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.982Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4c86074f-ca9c-4406-9778-b9e888d32c03","format_issues":null,"number":10849} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2ed1e1 | problem | aim-0df1011a6fa8a3c46e2c977b7e2ed1e1 | Random graph labeling | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Given a graph $G$ with random vertex label, determine the probability that $G$ is radio labeled. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2ed1e1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2ed1e1",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2ed1e1",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.988Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"19a12fc8-6ea3-4dc4-8378-dc903287e8c2","format_issues":null,"number":10850} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2efa2f | problem | aim-0df1011a6fa8a3c46e2c977b7e2efa2f | Distance antimagic labeling | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | A graph is distance antimagic if and only if all the vertices have a distinct neighborhood. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2efa2f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2efa2f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2efa2f",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.998Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"76da4b8c-c3f8-4f90-acd2-afedc471ed38","format_issues":null,"number":10851} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2f4adc | problem | aim-0df1011a6fa8a3c46e2c977b7e2f4adc | Distance magic labeling | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Let $r$ be even and $n$ be odd. For a $r$-regular graph of order $n$, determine if such a labeling exists. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2f4adc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Bryan Freyberg | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e2f4adc",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2f4adc",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.004Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"194e924b-c005-401b-b2c3-fb95f49bcfc5","format_issues":null,"number":10852} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2f888c | problem | aim-0df1011a6fa8a3c46e2c977b7e2f888c | Power domination with zero forcing variants | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine the minimum number of elements in a set $S$ so that such a propagation process covers the vertices of $G$ after a time step $t \in \mathbb{N}$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f888c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Adam Berliner | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f888c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2f888c",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.017Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"20569304-cbf4-47ab-a6ab-a93f61ec6c79","format_issues":null,"number":10854} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2f966f | problem | aim-0df1011a6fa8a3c46e2c977b7e2f966f | Reversible zero forcing | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | For $t=3$ and a graph $G$, determine the minimum number of elements in a set $S \subseteq V(G)$ so that such a propagation process covers the vertices of $G$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f966f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Daniela Ferrero | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f966f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2f966f",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.023Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1582044e-4bd0-4007-a837-8dea92e75f7f","format_issues":null,"number":10855} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2f9a08 | problem | aim-0df1011a6fa8a3c46e2c977b7e2f9a08 | Zero forcing and planarity | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Let $G$ be a planar graph. Determine conditions for which a zero forcing set $S$ exists. If such a set $S$ exists, determine bounds on the size of the zero forcing set $S$ of $G$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f9a08",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Emily McMillon | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f9a08",
"note": null,
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{
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"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.030Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b3497e05-006f-4314-aee6-261e09808499","format_issues":null,"number":10856} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2f9d93 | problem | aim-0df1011a6fa8a3c46e2c977b7e2f9d93 | Power domination for $d$-regular random graphs | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine if the power domination result for $3$-regular random graphs can be generalized to $d$-regular random graphs. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f9d93",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Daniela Ferrero | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2f9d93",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2f9d93",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.036Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d757230e-60d5-48a3-9076-af10487cce42","format_issues":null,"number":10857} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2fa83d | problem | aim-0df1011a6fa8a3c46e2c977b7e2fa83d | Random forcing set | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Given a graph $G$ with a minimum zero forcing set of size $s_0$, determine the probability that a randomly chosen set $S$ of size $s \ge s_0$ is a forcing set. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fa83d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Amanda Redlich | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fa83d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2fa83d",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.041Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cab28b1f-a4bf-420c-9207-fc52a96758f4","format_issues":null,"number":10858} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2fb296 | problem | aim-0df1011a6fa8a3c46e2c977b7e2fb296 | Redefining as poset problems | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine conditions for a poset $(\mathcal{G}, \preceq)$ where $\mathcal{G}$ is the set of graphs with a minimum size power dominating (zero forcing) set. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fb296",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ann Trenk | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fb296",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2fb296",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.047Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d97c522d-dca6-4279-8ecd-471129446418","format_issues":null,"number":10859} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2fbe00 | problem | aim-0df1011a6fa8a3c46e2c977b7e2fbe00 | Proportional zero forcing | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine the minimum number of vertices needed to guarantee a graph to be fully forced. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fbe00",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Chassidy Bozeman | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e2fbe00",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2fbe00",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.053Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"735d8e99-a44b-457f-9537-c3cda656be0b","format_issues":null,"number":10860} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e30809d | problem | aim-0df1011a6fa8a3c46e2c977b7e30809d | Upper bound on the maximum nullity of a graph | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine if the enhanced (odd cycle) forcing number bounds the maximum nullity of any families of graphs. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e30809d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mark Hunnell | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e30809d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e30809d",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.059Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1dd49992-516b-4eca-bb33-fd48cdefc0b8","format_issues":null,"number":10861} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e309d49 | problem | aim-0df1011a6fa8a3c46e2c977b7e309d49 | Neighborhood balanced coloring | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine graphs that admit such a coloring. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e309d49",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
An edge-magic total (EMT) labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers {1,2,...,v+e} with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of ... | 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"
] | Alison Marr | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/1/#0df1011a6fa8a3c46e2c977b7e309d49",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e309d49",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.010Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"56cb133d-bd20-4072-a297-5f67f3732cd4","format_issues":null,"number":10853} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e30f252 | problem | aim-0df1011a6fa8a3c46e2c977b7e30f252 | Maximal zero forcing sets | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine if the zero forcing number is equivalent to the maximal number of zero forcing sets. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e30f252",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Section context
Given a simple, finite graph $G$ with vertex set $V(G)$, we define a zero forcing set of $G$ as follows. Choose $S \subseteq V(G)$ and color all vertices of $S$ blue and all vertices in $V(G)-S$ white. The color change rule is if $w$ is the only white neighbor of blue vertex $v$, then we change the ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/2/#0df1011a6fa8a3c46e2c977b7e30f252",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e30f252",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.065Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6af57045-c60b-4400-bf30-485e620f080a","format_issues":null,"number":10862} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e311d39 | problem | aim-0df1011a6fa8a3c46e2c977b7e311d39 | Thickness of a graph | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Characterize the nonplanar graphs that are thickness-$2$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e311d39",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Question context
The thickness of a graph is the minimum number of planar graphs into which the edges of G can be partitioned. A graph is thickness-$k$ if the minimum number of planar graphs into which the edges of G can be partitioned is $k$. | 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"
] | Christine Kelley | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e31336c | problem | aim-0df1011a6fa8a3c46e2c977b7e31336c | Minimum rank clique covers | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Given a graph $G$, determine if there exists a clique cover whose minimum rank matrices admit a minimum rank matrix of $G$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e31336c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · 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"
] | Mark Hunnell | null | null | null | [
{
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"128a465d-295f-499b-b1b3-3fbdce690b30","format_issues":null,"number":10864} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e313e22 | problem | aim-0df1011a6fa8a3c46e2c977b7e313e22 | Forbidden separation | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Given a forbidden set of nonnegative integers $S$, find an infinite sequence such that for any two numbers in the sequence, their difference is not in $S$. Furthermore, determine the density of the sequence. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e313e22",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · 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"
] | Daphne Liu | null | null | null | [
{
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"38fee149-a244-45e7-ac0f-5ad7c24eb276","format_issues":null,"number":10865} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e31512d | problem | aim-0df1011a6fa8a3c46e2c977b7e31512d | Permutation assignment on lift graphs | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Given a base graph $G$ with property $P$, determine if there exists a permutation assignment to the edge of the base graph such that the lift of the graph inherits property $P$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e31512d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Question context
For graphs $G$ and $H$, a covering map $f: V(H) \rightarrow V(G)$ is a surjection and a local isomorphism, that is, the neighborhood of a vertex $H$ in $G$ is mapped one-to-one onto the neighborhood of $f(v)$ in $G$. When such a mapping exists, we say that $H$ is a lift of $G$. The lift’s propertie... | 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"
] | Christine Kelley | null | null | null | [
{
"kind": "website",
"citation": "Graph Theory: structural properties, labelings, and connections to applications · Original question",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e31512d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1eb8f56b-b76d-4da6-8db2-7354db6ceae8","format_issues":null,"number":10866} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e316165 | problem | aim-0df1011a6fa8a3c46e2c977b7e316165 | Induced subgraphs | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine the possible induced subgraphs of $G$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e316165",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Question context
Let $d < k < \binom{n}{2}$ and let $G$ be a bipartite graph with partite sets $X$ and $Y$ where the vertices in $X$ correspond to all possible $d$ subsets of $[n]$ and the vertices in $Y$ correspond to all possible $k$ subsets of $[n]$. For $x \in X$ and $y \in Y$, the edge $xy \in E(G)$ if $l(x) \... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Emily McMillon | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e316165",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"bbdd8bc8-48b8-4362-85b6-c168e0098564","format_issues":null,"number":10867} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e31628a | problem | aim-0df1011a6fa8a3c46e2c977b7e31628a | Graph Homomorphisms | {
"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/graphstructureapp/ Not an author-supplied MSC code."
}
] | Determine a family of trees $\mathscr{T}$ that admits the minimum cardinality of $S$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Graph Theory: structural properties, labelings, and connections to applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e31628a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Graph Theory: structural properties, labelings, and connections to applications · AIMPL workshop record | ## Question context
The homomorphisms of a graph $G$ give information on various invariants of $G$. For example, a $k$-coloring of $G$ is equivalent to a homomorphism $G \rightarrow K_k$. For a given tree $T$, we consider the set of homomorphisms $T \rightarrow G$. Let $S$ be the set of homomorphisms $T \rightarrow G$... | 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"
] | David Galvin | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/graphstructureapp/3/#0df1011a6fa8a3c46e2c977b7e31628a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b38526f4-8c9d-49ef-a0f6-0294d75e7ae9","format_issues":null,"number":10868} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e333b2a | problem | aim-0df1011a6fa8a3c46e2c977b7e333b2a | Kahler Currents | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Show that singular Kahler-Einstein metrics (or more generally singular cscK metrics) are in fact Kahler currents. This was shown in [GGZ] (2022) under suitable assumptions. This is known in dimension $\leq 3$, but it would be nice to understand it more generally.
One could also ask this for singular Kahler almost-Eins... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e333b2a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Gabor Szekelyhidi | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e333b2a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url": "http://aimp... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c32c4357-c2fa-41d8-991f-f1931a8f32d1","format_issues":null,"number":11430} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33422a | problem | aim-0df1011a6fa8a3c46e2c977b7e33422a | Regularity of Kahler-Einstein Metrics | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Are the local potentials of a singular Kahler-Einstein metric Holder continuous (with respect to the Fubini-Study metric), given that the singularity is smoothable?
This is known in certain cases near isolated singularities by Hein-Sun and Chiu-Szekelyhidi. | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e33422a",
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Jian Song | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e33422a",
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},
{
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"url": "http://aimp... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"88ee6342-3a4b-47d8-bc96-1046456e152a","format_issues":null,"number":11431} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33507b | problem | aim-0df1011a6fa8a3c46e2c977b7e33507b | Convexity of the Regular Set | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Is the regular set of a singular Kahler-Einstein manifold $(X,\omega_{KE})$ convex? That is, is it true that for any two points $x,y\in X_{\text{reg}}$, there is a minimal geodesic in $X$ from $x$ to $y$ which lies entirely in $X_{\text{reg}}$? This is known to be true if $X$ is a Gromov-Hausdorff limit of a sequence o... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e33507b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"37b23651-fb2a-4157-88f5-379943f028f0","format_issues":null,"number":11432} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e335e93 | problem | aim-0df1011a6fa8a3c46e2c977b7e335e93 | Uniform Bounds in Families | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Problem 5. Let $X$ be a connected component of the moduli space of Kahler-Einstein metrics on a compact complex manifold Y of general type, and let $\pi:\mathcal{X}\to X$ be the corresponding universal family. Then there exists $N\in\mathbb{N}$ and a closed embedding $\iota:\mathcal{X}\hookrightarrow X\times\mathbb{P}^... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e335e93",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Jacob Sturm | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/1/#0df1011a6fa8a3c46e2c977b7e335e93",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
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"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.448Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e1563156-c2c0-4dee-895a-7a6cbb082bf2","format_issues":null,"number":11433} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33769e | problem | aim-0df1011a6fa8a3c46e2c977b7e33769e | Volume Bounds for Sublevel Sets | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | It is known that given a bounded pseudoconvex domain $\Omega\subseteq\mathbb{C}^{n}$,
there exist $C=C(\Omega)$ and $\alpha=\alpha(\Omega)$ such that
for any $u\in PSH(\Omega)$ satisfying $u|_{\partial\Omega}\equiv0$
and $\int_{\Omega}(dd^{c}u)^{n}=1$ (and this is defined), we have
$$
\int_{\Omega}e^{-\alpha u}\omega... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e33769e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Sławomir Kołodziej | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e33769e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e33769e",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.455Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5708624d-894b-4f05-8e0d-226c359f36d7","format_issues":null,"number":11434} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e338735 | problem | aim-0df1011a6fa8a3c46e2c977b7e338735 | C^0 Bounds for Complex Hessian Equations | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Suppose $(X,\omega_{X})$ is a Kahler manifold and $\omega_{0}$ is
another Kahler metric on $X$. Suppose $C_{1}<\infty$ satisfies
$$
\omega_{X}\leq C_{1}\omega_{0}.
$$
Let $u\in C^{\infty}(X)$, and let $\lambda[u]$ be the eigenvalues
of $\omega_{0}+\sqrt{-1}\partial\overline{\partial}u$ with respect
to $\omega_{X}$... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e338735",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Tat Dat TÔ | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e338735",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e338735",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.462Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"42bf0769-5796-43e2-a9d7-f193475059f8","format_issues":null,"number":11435} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e339c89 | problem | aim-0df1011a6fa8a3c46e2c977b7e339c89 | Gradient Estimate | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Consider the equation
$$
F[\lambda[u]]=\psi,
$$
where $\omega_{0},\omega_{X}$ are nonnegative Hermitian $(1,1)$-forms
and $\lambda[u]$ are the eigenvalues of $\omega_{0}+\sqrt{-1}\partial\overline{\partial}u$
with respect to $\omega_{X}$. Assume the $C$-subsolution condition
holds, and that $F$ is concave. Is it po... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e339c89",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Bin Guo | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e339c89",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e339c89",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.467Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b581fb5a-88ec-440a-9ebf-a481a3d30f81","format_issues":null,"number":11436} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33a486 | problem | aim-0df1011a6fa8a3c46e2c977b7e33a486 | Liouville Property | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Suppose $\det(\partial_{i}\partial_{\overline{j}}u)=1$ on $\mathbb{C}^{n}$
and
$$
C^{-1}(1+|z|^{2})\leq\partial_{i}\partial_{\overline{j}}u(z)\leq C(1+|z|^{2})
$$
for all $z\in\mathbb{C}^{n}$. Is it true that $u$
It known if, in addition, $\sqrt{-1}\partial\overline{\partial}u$
is a complete Kahler metric on $\m... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e33a486",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/2/#0df1011a6fa8a3c46e2c977b7e33a486",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e33a486",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.476Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"649ffe14-1f25-4088-89a5-54a605b35f05","format_issues":null,"number":11437} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33af0f | problem | aim-0df1011a6fa8a3c46e2c977b7e33af0f | Flow Convergence from Perturbation of Elliptic Solution | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Suppose $(M,\omega)$ is a complete Kaher manifold with bounded geometry,
and $u\in C^{\infty}(M)$ solves
$$
(\omega+\sqrt{-1}\partial\overline{\partial}u)^{n}=e^{f}\omega^{n},
$$
and satisfies
$$
C^{-1}\omega\leq\omega+\sqrt{-1}\partial\overline{\partial}u\leq C\omega
$$
$$
|f|(z)\leq\frac{C}{d_{\omega}^{... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33af0f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Albert Chau | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33af0f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e33af0f",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.482Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f538c4ae-96b0-4d28-ba43-f94a6d531ac1","format_issues":null,"number":11438} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33b41a | problem | aim-0df1011a6fa8a3c46e2c977b7e33b41a | Kahler-Ricci Tangent Flows | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Given a closed Kahler-Ricci flow $(M,(\omega_{t})_{t\in[0,T)})$,
under what conditions are tangent flows complex analytic spaces? It
is known if $M$ is Fano or if $n=2$. It is conjectured to be true
starting with any projective Kahler-Ricci flow.
What about given a limit of polarized Kahler-Ricci flows? With extra
ass... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33b41a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Max Hallgren | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33b41a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e33b41a",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.488Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c19111e-1a0f-42a8-bfcf-71fbf7beca01","format_issues":null,"number":11439} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33bea2 | problem | aim-0df1011a6fa8a3c46e2c977b7e33bea2 | Maximal Existence Time for Pluriclosed Flow | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | A pluriclosed metric is a positive $(1,1)$-form $\eta$ such that
$\sqrt{-1}\partial\overline{\partial}\eta=0$. The pluriclosed flow
is
$$
\partial_{t}\eta=(Rc_{B}(\eta_{t}))^{1,1},
$$
where $Rc_{B}$ is the Ricci curvature of the Bismut connection. Short
time existence is known, and there is an upper bound on the f... | unassessed | {
"key": "aimpl",
"name": "AIMPL · PDE methods in complex geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33bea2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | PDE methods in complex geometry · 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"
] | Anna Fino | null | null | null | [
{
"kind": "website",
"citation": "PDE methods in complex geometry · Original question",
"url": "http://aimpl.org/pdecomplexgeom/3/#0df1011a6fa8a3c46e2c977b7e33bea2",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e33bea2",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.493Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3b51a058-6c03-4d39-8b63-b7a0058c8690","format_issues":null,"number":11440} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33ce22 | problem | aim-0df1011a6fa8a3c46e2c977b7e33ce22 | Expanding Solitons from Divisorial Contractions | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Consider a Kahler-Ricci Flow $(M^{2},(g_{t})_{t\in[0,T)})$ developing a finite-time
singularity with $\lim_{t\to T}\text{Vol}_{\omega_{t}}(M)>0$. Doing
a Type-I blowup backwards in time, is the flow coming out of the singularity
Cao's expanding soliton?
In the Riemannian case, one can flow out of isolated cone singula... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | Max Hallgren | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e33f4ec | problem | aim-0df1011a6fa8a3c46e2c977b7e33f4ec | Diameter of Moduli of Kahler-Einstein Metrics of General Type | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Does the moduli space of Kahler-Einstein manifolds of general type
equipped with the Weil-Petersen metric have bounded diameter? It is
known that local potentials are continuous up to the boundary. Also,
is the $p$-Nash entropy of the Weil-Petersen metric bounded (with
respect to the Euclidean reference metric)?
This ... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | Jacob Sturm | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34118b | problem | aim-0df1011a6fa8a3c46e2c977b7e34118b | Properness of Harmonic Map Energy | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
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"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | Given a Teichmuller space of Kahler-Einstein manifolds (this is the
universal cover of the moduli space) of general type, the energy functional
for maps into a Riemannian manifold with Hermitian nonpositive curvature
is plurisubharmonic. Is this functional also proper? This is related
to degenerations of Kahler-Einstei... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Yingying Zhang | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e341c35 | problem | aim-0df1011a6fa8a3c46e2c977b7e341c35 | Long-Time Existence of Complete Noncompact Kahler-Ricci Flow | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "32",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code."
}
] | If $\sqrt{-1}\partial\overline{\partial}u$ is complete and $U(n)$-invariant
Kahler metric on $\mathbb{C}^{n}$, does there exist a solution to
the Kahler-Ricci flow?
This is known if $\sqrt{-1}\partial\overline{\partial}u$ has nonnegative
holomorphic bisectional curvature. | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Albert Chau | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e346201 | problem | aim-0df1011a6fa8a3c46e2c977b7e346201 | Exact sequences of Hopf algebras | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Consider an exact sequence of Hopf algebras $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$, where $B$ is finite-dimensional. If $A$ and $C$ satisfy the FGC conjecture, does $B$ satisfy it as well?
- Consider a supergroup scheme $G$. Does the Drinfeld double satisfy the FGC conjecture? (It ... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to FGC conjecture for Hopf algebras | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
For recent progress, see https://arxiv.org/abs/2407.05881. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nicolas Andruskiewitsch | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3469fa | problem | aim-0df1011a6fa8a3c46e2c977b7e3469fa | FGC for Hopf algebras · Question 1.2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
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}
] | Let $B$ be a finite-dimensional bialgebra over a field $\mathbf{k}$. What are examples of $B$ for which the FGC conjecture is not true? | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to FGC conjecture for Hopf algebras | 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"
] | Hector Pena Pollastri | null | null | null | [
{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e346a53 | problem | aim-0df1011a6fa8a3c46e2c977b7e346a53 | FGC for Hopf algebras · Question 1.3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $H$ be a finite-dimensional Hopf algebra. Let $\mathcal{C}$ denote the semisimplification of its representation category. Does $\mathcal{C}$ have nice subcategories $\mathcal{D}$? Consider Hopf algebras of tame representation type and their semisimplifications. | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to FGC conjecture for Hopf algebras | 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"
] | Nicolas Andruskiewitsch | null | null | null | [
{
"kind": "website",
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"note": null,
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{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e347ec5 | problem | aim-0df1011a6fa8a3c46e2c977b7e347ec5 | FGC for tensor categories · Question 2.1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
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"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | If $\mathcal{C}$ satisfies the FGC conjecture and $\mathcal{B} \subset \mathcal{Z}(\mathcal{C})$, is it true that the M\"uger centralizer $\mathcal{Z}_{(2)}(\mathcal{B} \subset \mathcal{Z}(\mathcal{C}))$ also satisfies the FGC conjecture? | unassessed | {
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"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Categorical questions related to FGC conjecture for Hopf algebras. | 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"
] | Hector Pena Pollastri | null | null | null | [
{
"kind": "website",
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e349381 | problem | aim-0df1011a6fa8a3c46e2c977b7e349381 | FGC for Hopf algebras · Question 1.4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
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}
] | Does there exist a scheme parameterizing types of Hopf algebras? (Nichols algebras would be one of the types.) | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to FGC conjecture for Hopf algebras | 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"
] | Karin Erdmann | null | null | null | [
{
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... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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] | [] | {
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"updated_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"20e30380-523d-4233-bb07-e83287c842d5","format_issues":null,"number":10616} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34ad89 | problem | aim-0df1011a6fa8a3c46e2c977b7e34ad89 | Miscellaneous · Question 5.1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Calculate the Gerstenhaber bracket of the Yoneda algebra in examples. (e.g.~for $\mathcal{C} = \text{Comod}(\mathcal{U}(\mathfrak{g}))$, the Yondea algebra is $\wedge(\mathfrak{g})$ and the bracket is the one in degree 1.) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/5/#0df1011a6fa8a3c46e2c977b7e34ad89",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · 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"
] | Alexei Davydov | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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{
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... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"source-full-text-not-present"
] | [] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2dc7207a-d3d2-4a67-909c-2bbf3d8a55a8","format_issues":null,"number":10632} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34bc54 | problem | aim-0df1011a6fa8a3c46e2c977b7e34bc54 | Balmer spectrum/TTG · Question 3.1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Compute the Balmer spectrum of the stable module categories of some pointed Hopf algebras of tame type in characteristic $0$ (e.g.~$u_q(\mathfrak{sl}(1|2))$). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e34bc54",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | 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"
] | Vera Serganova | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e34bc54",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.660Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0c0f7e2e-78e5-458c-9173-5a9bf1840161","format_issues":null,"number":10623} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34bee3 | problem | aim-0df1011a6fa8a3c46e2c977b7e34bee3 | FGC for tensor categories · Question 2.2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Is there a nice class of categories where the FGC conjecture holds? (Something larger than the class of finite tensor categories.) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/2/#0df1011a6fa8a3c46e2c977b7e34bee3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Categorical questions related to FGC conjecture for Hopf algebras. | 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"
] | Paul Balmer | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/2/#0df1011a6fa8a3c46e2c977b7e34bee3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e34bee3",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.643Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d61411d9-f4c9-460a-9ca1-1077083a3ee6","format_issues":null,"number":10620} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34c583 | problem | aim-0df1011a6fa8a3c46e2c977b7e34c583 | Balmer spectrum/TTG · Question 3.2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $\mathcal{C}$ be a symmetric FTC. Is it true that $\text{Spc}(\text{St}(\mathcal{C})) = \text{Proj}(\text{Ext}^*_{\mathcal{C}}(\mathbf{1}))$? (This is known for cocommutative Hopf algebras.) In the non-braided case, is it true that $\text{Spc}(\text{St}(\mathcal{C})) = \text{Proj}(\text{some particular subalgebra o... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e34c583",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | 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"
] | Kent Varshaw | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e34c583",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e34c583",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.667Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b14bbf96-a9c8-4f7d-8aa6-2b7b62d79164","format_issues":null,"number":10624} |
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