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1.0.0 | problem:3sum-conjecture | problem | 3sum-conjecture | The 3SUM conjecture | {
"main": "computer science",
"sub": "algorithms",
"slug": "algorithms",
"name": "Algorithms and data structures",
"original_discipline": "computer-science"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
},
{
"main": "computer science",
"sub": "computational geometry",
"slug": "computational-geometry",
... | [
{
"code": "68W",
"basis": "community-map",
"evidence": "Inferred from community field: algorithms"
}
] | Given $n$ integers, decide whether some three of them sum to zero. Conjecture: no algorithm solves 3SUM in time $O(n^{2-\varepsilon})$ for any $\varepsilon > 0$ on a word RAM with $O(\log n)$-bit words. | open | {
"key": "community",
"name": "Community consensus",
"type": "journal",
"url": null,
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Original wording",
"notes": "Questions that are widely regarded as open but have no single canonical citation; written here from the surrounding literature.... | null | null | null | not-recorded | not-recorded | null | [] | [] | Is there any truly subquadratic algorithm for finding three numbers summing to zero? | 3SUM is the anchor of fine-grained complexity: dozens of problems in computational geometry and string algorithms have been shown to require quadratic time unless 3SUM does not. The conjecture plays the role $\mathrm{P}\ne\mathrm{NP}$ plays for NP-hardness, but at the level of polynomial exponents. | - Grønlund and Pettie (2014) gave an $O(n^2/(\log n / \log\log n)^{2/3})$ algorithm, showing the exact quadratic bound is false, though the improvement is subpolynomial.
- Chan improved the polylogarithmic savings further.
- In the decision-tree model, $O(n^{3/2})$ comparisons suffice (Kane, Lovett, Moran), which shows... | null | published | sharp | hard | [
"conditional-hardness",
"fine-grained-complexity",
"lower-bounds"
] | Gajentaan and Overmars lineage | 1,995 | null | null | [] | {
"source_record": null,
"imported_at": null,
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"evidence_label": null,
"note": null,
"has_full_text": null,
"original_file": null,
"sha256": null
} | null | [] | [] | {
"created_at": "2026-09-07T23:45:31.857Z",
"updated_at": "2026-09-07T23:45:31.857Z",
"published_at": "2026-09-07T23:45:35.135Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c669653d-2ce1-402c-8459-2c639e221cda","format_issues":null,"number":32} |
1.0.0 | problem:aaronson-2021-1 | problem | aaronson-2021-1 | An oracle separating QMA from QCMA | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 1
Is there an oracle relative to which $\mathsf{QMA}\neq\mathsf{QCMA}$? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 1",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem1",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 1, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | An oracle separating QMA from QCMA — original question and dated source context. | ## Context from the 2021 source
2 $\mathsf{QMA}$ and Oracle Separations
Recall that $\mathsf{QMA}$, Quantum Merlin Arthur, is the class of languages $L$ for which membership in $L$ can be proven via a polynomial-size quantum witness state $\left|\varphi\right\rangle$ that’s verified in quantum polynomial time. In 200... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 1",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem1",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem1",
"imported_at": "2026-09-08",
"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.405Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c8c3689f-4794-46ca-b380-f709f92cb8ae","format_issues":null,"number":9415} |
1.0.0 | problem:aaronson-2021-10 | problem | aaronson-2021-10 | Finding an explicit path through glued trees | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | In the glued-trees oracle graph of Childs et al. (2002), with two depth-$n$ binary trees joined at their leaves as described in section 8 of the source, consider the task of producing an explicit entrance-to-exit path.
Problem 10
Suppose, however, that we actually want to find a path from left to right. Does even a q... | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 10",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem10",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 10, 2021-09-14.",
"doi": ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finding an explicit path through glued trees — original question and dated source context. | ## Context from the 2021 source
8 Glued Trees
In 2002, Childs et al. [[25](<https://arxiv.org/html/2109.06917v1#bib.bib25>)] gave a celebrated quantum walk algorithm that, informally, gets from the leftmost to the rightmost vertex in the following $\exp\left(n\right)$-sized graph, in only $\operatorname*{poly}\left(n... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 10",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem10",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem10",
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"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.451Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bbb50d44-e447-43f3-b991-0a14d8a8c5c4","format_issues":null,"number":9424} |
1.0.0 | problem:aaronson-2021-11 | problem | aaronson-2021-11 | Standard versus erasing quantum oracles | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 11
Are there sets of injective functions $f$ for which a quantum computer can learn certain properties of $f$ using few queries to a standard oracle, but not using few queries to an erasing oracle? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 11",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem11",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 11, 2021-09-14.",
"doi": ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Standard versus erasing quantum oracles — original question and dated source context. | ## Context from the 2021 source
9 Comparing Query Models
Given a function $f$, the usual model of quantum query complexity is that we get access to an oracle that maps basis states of the form $\left|x,a\right\rangle$ to basis states of the form $\left|x,a\oplus f\left(x\right)\right\rangle$, where $\oplus$ denotes b... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 11",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem11",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem11",
"imported_at": "2026-09-08",
"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.456Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7654d444-e1ff-43fa-8373-c6cad2b2fa0d","format_issues":null,"number":9425} |
1.0.0 | problem:aaronson-2021-12 | problem | aaronson-2021-12 | Quantum queries beyond the Fourier-sampling cross-entropy benchmark | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Given query access to $f:\{0,1\}^n\to\{-1,1\}$, let $\widehat f$ denote its Boolean Fourier coefficients and define $\chi=(2^n/k)\sum_{i=1}^k\widehat f(s_i)^2$. The source compares this with ordinary Fourier sampling, which achieves $\chi\approx3$.
Problem 12
What is the quantum query complexity of outputting samples... | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 12",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem12",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 12, 2021-09-14.",
"doi": ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Quantum queries beyond the Fourier-sampling cross-entropy benchmark — original question and dated source context. | ## Context from the 2021 source
10 The Linear Cross-Entropy Benchmark
In Fall 2019, a team at Google reported the achievement of quantum supremacy based on a sampling benchmark with superconducting qubits [[27](<https://arxiv.org/html/2109.06917v1#bib.bib27>)]. In Summer 2021, a team at USTC in China reported an inde... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 12",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem12",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem12",
"imported_at": "2026-09-08",
"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.461Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0cb55482-33d5-40bb-8b87-e80bfd479f41","format_issues":null,"number":9426} |
1.0.0 | problem:aaronson-2021-2 | problem | aaronson-2021-2 | An oracle separating QMA from QMA(2) | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 2
Is there an oracle—even a quantum oracle—relative to which $\mathsf{QMA}\neq\mathsf{QMA}\left(2\right)$? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 2",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem2",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 2, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | An oracle separating QMA from QMA(2) — original question and dated source context. | ## Context from the 2021 source
2 $\mathsf{QMA}$ and Oracle Separations
Recall that $\mathsf{QMA}$, Quantum Merlin Arthur, is the class of languages $L$ for which membership in $L$ can be proven via a polynomial-size quantum witness state $\left|\varphi\right\rangle$ that’s verified in quantum polynomial time. In 200... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 2",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem2",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem2",
"imported_at": "2026-09-08",
"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.410Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d77a8e5a-9da9-4382-9ea9-d88771094174","format_issues":null,"number":9416} |
1.0.0 | problem:aaronson-2021-3 | problem | aaronson-2021-3 | Query–memory tradeoffs for collision and element distinctness | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 3
What are the optimal tradeoffs between the number of queries used by a quantum algorithm to solve the collision or the element distinctness problems, and the number of qubits or classical bits of memory? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 3",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem3",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 3, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | Query–memory tradeoffs for collision and element distinctness — original question and dated source context. | ## Context from the 2021 source
3 Query/Space Tradeoffs
In the collision problem, we’re given black-box access to a function $f:\left\{1,\ldots,n\right\}\rightarrow\left\{1,\ldots,m\right\}$ (where $n$ is even and $m\geq n$), and are asked to decide whether $f$ is 1-to-1 or 2-to-1, promised that one of those is the c... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 3",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem3",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem3",
"imported_at": "2026-09-08",
"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.419Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8e5c9c57-6637-4d72-bb45-8fa4ea4b0ad4","format_issues":null,"number":9417} |
1.0.0 | problem:aaronson-2021-4 | problem | aaronson-2021-4 | Maximal randomized–quantum separation for total Boolean functions | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 4
What is the largest possible gap between $\operatorname*{R}\left(f\right)$ and $\operatorname*{Q}\left(f\right)$, for a total Boolean function $f$? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 4",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem4",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 4, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | Maximal randomized–quantum separation for total Boolean functions — original question and dated source context. | ## Context from the 2021 source
4 Maximal Separations
Given a total Boolean function $f:\left\{0,1\right\}^{n}\rightarrow\left\{0,1\right\}$, we denote by $\operatorname*{D}\left(f\right)$, $\operatorname*{R}\left(f\right)$, and $\operatorname*{Q}\left(f\right)$ the deterministic, (bounded-error) randomized, and (bou... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 4",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem4",
"note": null,
"sort_order": 0
}
] | {
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"status_as_of": "2021-09-14",
"evidence_label": "Historical source; current status unassessed",
"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.423Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cfe574d5-fc91-495d-a324-654ce834750b","format_issues":null,"number":9418} |
1.0.0 | problem:aaronson-2021-5 | problem | aaronson-2021-5 | Quantum queries versus approximate degree for partial functions | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 5
What is the largest possible gap between $\operatorname*{Q}\left(f\right)$ and $\widetilde{\deg}\left(f\right)$ for partial $f$? Can the gap even be exponential? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 5",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem5",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 5, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | Quantum queries versus approximate degree for partial functions — original question and dated source context. | ## Context from the 2021 source
5 Degree of Partial Functions
Let $f:S\rightarrow\left\{0,1\right\}$ be a partial Boolean function, where $S\subseteq\left\{0,1\right\}^{n}$. Define the approximate degree of $f$, or $\widetilde{\deg}\left(f\right)$, to be the minimum degree of a real polynomial $p:\mathbb{R}^{n}\right... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 5",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem5",
"note": null,
"sort_order": 0
}
] | {
"source_record": "https://arxiv.org/html/2109.06917v1#Thmtheorem5",
"imported_at": "2026-09-08",
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"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1e771742-e685-4277-a329-8f2c6fbdcc09","format_issues":null,"number":9419} |
1.0.0 | problem:aaronson-2021-6 | problem | aaronson-2021-6 | Unitary synthesis with a classical oracle | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 6
For every $n$-qubit unitary transformation $U$, does there exist an oracle $A:\left\{0,1\right\}^{\ast}\rightarrow\left\{0,1\right\}$ such that a $\mathsf{BQP}^{A}$ machine can implement $U$?11 1 Technically, Kuperberg and I only asked whether this is true for a Haar-random U, but I expect the Haar-random ca... | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 6",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem6",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 6, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | Unitary synthesis with a classical oracle — original question and dated source context. | ## Context from the 2021 source
6 Unitary Synthesis Problem
In 2007, Greg Kuperberg and I [[8](<https://arxiv.org/html/2109.06917v1#bib.bib8>)] raised the following question:
Problem 6
For every $n$-qubit unitary transformation $U$, does there exist an oracle $A:\left\{0,1\right\}^{\ast}\rightarrow\left\{0,1\right\... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 6",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem6",
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... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4c773bfd-6628-4aa0-9b76-0a7d3a165eb4","format_issues":null,"number":9420} |
1.0.0 | problem:aaronson-2021-7 | problem | aaronson-2021-7 | An oracle separating BQP from IP | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 7
Does there exist an oracle $A$ such that $\mathsf{BQP}^{A}\not\subset\mathsf{IP}^{A}$? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 7",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem7",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 7, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | An oracle separating BQP from IP — original question and dated source context. | ## Context from the 2021 source
7 Verifiability of Quantum Computing
Let $\mathsf{IP}$ be the class of languages that admit classical interactive proofs. In the unrelativized world, $\mathsf{IP}=\mathsf{PSPACE}$ [[45](<https://arxiv.org/html/2109.06917v1#bib.bib45>)], but it’s well-known that the situation relative t... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
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"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
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"created_at": "2026-09-08T04:57:39.703Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"994f11b2-cd53-48c4-94be-46879b1db418","format_issues":null,"number":9421} |
1.0.0 | problem:aaronson-2021-8 | problem | aaronson-2021-8 | An oracle separating BQP from interactive proofs with BQP provers | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 8
Is there at least an oracle relative to which $\mathsf{BQP}\neq\mathsf{IP}_{\mathsf{BQP}}$? | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 8",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem8",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 8, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | An oracle separating BQP from interactive proofs with BQP provers — original question and dated source context. | ## Context from the 2021 source
7 Verifiability of Quantum Computing
Let $\mathsf{IP}$ be the class of languages that admit classical interactive proofs. In the unrelativized world, $\mathsf{IP}=\mathsf{PSPACE}$ [[45](<https://arxiv.org/html/2109.06917v1#bib.bib45>)], but it’s well-known that the situation relative t... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
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"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
"current-status-unassessed"
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"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.442Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"a3be0351-38c4-4dbc-aa60-e928b47442e3","format_issues":null,"number":9422} |
1.0.0 | problem:aaronson-2021-9 | problem | aaronson-2021-9 | Relativization of blind and verified quantum computation | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [
{
"main": "computer science",
"sub": "computational complexity",
"slug": "computational-complexity",
"name": "Computational complexity",
"original_discipline": "computer-science"
}
] | [] | Problem 9
Are the celebrated protocols for blind and verified quantum computation, due to Broadbent et al. [[23](<https://arxiv.org/html/2109.06917v1#bib.bib23>)], Aharonov et al. [[11](<https://arxiv.org/html/2109.06917v1#bib.bib11>)], and Mahadev [[41](<https://arxiv.org/html/2109.06917v1#bib.bib41>)], inherently no... | unassessed | {
"key": "aaronson-quantum",
"name": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 9",
"type": "survey",
"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem9",
"citation": "Scott Aaronson, Open Problems Related to Quantum Query Complexity, Problem 9, 2021-09-14.",
"doi": nul... | null | null | null | not-recorded | not-recorded | null | [] | [] | Relativization of blind and verified quantum computation — original question and dated source context. | ## Context from the 2021 source
7 Verifiability of Quantum Computing
Let $\mathsf{IP}$ be the class of languages that admit classical interactive proofs. In the unrelativized world, $\mathsf{IP}=\mathsf{PSPACE}$ [[45](<https://arxiv.org/html/2109.06917v1#bib.bib45>)], but it’s well-known that the situation relative t... | Historical source dated 2021-09-14. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date. | null | published | sharp | hard | [
"quantum-query-complexity"
] | Scott Aaronson | 2,021 | null | null | [
{
"kind": "paper",
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"url": "https://arxiv.org/html/2109.06917v1#Thmtheorem9",
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"note": "Numbered question with its source context. Importing a question does not certify that it remains open.",
... | null | [
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"created_at": "2026-09-08T04:57:39.703Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"dc62471a-bada-438c-92e2-b59f73e5bdbb","format_issues":null,"number":9423} |
1.0.0 | problem:abc-conjecture | problem | abc-conjecture | The abc conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "community-map",
"evidence": "Inferred from community field: number-theory"
}
] | For coprime positive integers $a + b = c$, let $\operatorname{rad}(n)$ denote the product of the distinct primes dividing $n$. The conjecture asserts that for every $\varepsilon > 0$ there are only finitely many triples with
$$c > \operatorname{rad}(abc)^{1+\varepsilon}.$$ | disputed | {
"key": "community",
"name": "Community consensus",
"type": "problem-list",
"url": null,
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Original wording",
"notes": "Questions that are widely regarded as open but have no single canonical citation; written here from the surrounding litera... | null | null | null | not-recorded | not-recorded | null | [] | [] | A claimed proof exists and is not accepted by the wider community — the conjecture's status is genuinely contested. | Formulated by Oesterlé and Masser in the mid-1980s. Shinichi Mochizuki announced a proof via inter-universal Teichmüller theory in 2012; it was published in *Publications of the RIMS* in 2021. Peter Scholze and Jakob Stix published a report identifying what they consider a gap in Corollary 3.12, which Mochizuki dispute... | - Weaker exponential bounds are known via Baker's theory of linear forms in logarithms.
- The function-field analogue (the Mason–Stothers theorem) is elementary and true.
- The dispute is documented publicly: see the Scholze–Stix report and Mochizuki's replies. | The conjecture implies Fermat's Last Theorem for large exponents, the Mordell conjecture (Faltings' theorem) with effective constants, Roth's theorem, and a long list of Diophantine statements. Its contested status is also a case study in how a community decides that something has been proved. | published | sharp | notorious | [
"contested",
"diophantine",
"iut"
] | Joseph Oesterlé and David Masser | 1,985 | null | null | [
{
"kind": "paper",
"citation": "P. Scholze, J. Stix, Why abc is still a conjecture (report, 2018).",
"url": null,
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} | null | [] | [] | {
"created_at": "2026-09-07T23:45:31.857Z",
"updated_at": "2026-09-07T23:45:31.857Z",
"published_at": "2026-09-07T23:45:34.905Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6c144b9e-6eb7-4afb-8abe-85c6e7e5e1ca","format_issues":null,"number":8} |
1.0.0 | problem:additivity-of-minimum-output-entropy | problem | additivity-of-minimum-output-entropy | Additivity of the minimum output entropy of quantum channels | {
"main": "physics",
"sub": "quantum information",
"slug": "quantum-information",
"name": "Quantum information",
"original_discipline": "physics"
} | [] | [] | For quantum channels $\Phi, \Psi$, is the minimum output von Neumann entropy additive,
$$S_{\min}(\Phi \otimes \Psi) = S_{\min}(\Phi) + S_{\min}(\Psi)?$$ | solved | {
"key": "community",
"name": "Community consensus",
"type": "journal",
"url": null,
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Original wording",
"notes": "Questions that are widely regarded as open but have no single canonical citation; written here from the surrounding literature.... | null | null | null | not-recorded | not-recorded | null | [] | [] | Everyone expected additivity. Hastings produced a random counterexample, and the classical capacity of a quantum channel became genuinely hard. | Additivity was the central conjecture of quantum Shannon theory in the 2000s, equivalent to additivity of the Holevo capacity and hence to the classical capacity of a quantum channel being given by a single-letter formula. Shor proved the equivalence of several additivity conjectures. Hastings disproved additivity in 2... | - Disproved: Hastings (2009), with the violation exponentially small in the dimension and established non-constructively.
- No explicit counterexample of moderate dimension is known; producing one is an open sub-problem.
- Whether the classical capacity is computable at all remains open, and related quantities have bee... | The failure of additivity means entangled inputs across channel uses can strictly increase the transmissible classical information, and that the classical capacity has no known finite-dimensional characterisation. It is the reason capacity computation remains open. | published | sharp | hard | [
"channel-capacity",
"random-constructions",
"resolved",
"shannon-theory"
] | Peter Shor lineage | 2,003 | null | null | [
{
"kind": "paper",
"citation": "M. B. Hastings, Superadditivity of communication capacity using entangled inputs, Nature Physics 5 (2009), 255–257.",
"url": "https://arxiv.org/abs/0809.3972",
"note": null,
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} | 2026-10-10T16:07:49.246Z | {"database_id":"510a2f2d-ef79-4321-b981-07e1b8bb4f53","format_issues":null,"number":56} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00396a | problem | aim-03c32d520917a449e9e2d9c17d00396a | Moduli height | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Let $X$ be a quasi-projective variety and $G$ a group action on $X$. Let $Y=X//G$ be a geometric quotient of $X$ by $G$. Is $h_Y(x) \asymp \min_{g \in G} h_X(gx)$? (ample heights)
In particular, fix an embedding $M_d \subset \mathbb{P}^M$. Then define a height $h_M:M_d \to \mathbb{R}$ using the embedding. Is this ... | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/1/#03c32d520917a449e9e2d9c17d00396a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/1/",
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.276Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e7051850-0ffd-49af-98d9-b509199e7ab5","format_issues":null,"number":7137} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d004ca6 | problem | aim-03c32d520917a449e9e2d9c17d004ca6 | Critical height conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Let $f:\mathbb{P}^1 \to \mathbb{P}^1$, not Latt\`es. Define the critical height
\begin{equation*}
\hat{h}_{crit}(f) = \sum_{c \in \text{crit}(f)} \hat{h}(c).
\end{equation*}
Does there exist $c_1,c_2 > 0$ depending on $d,h_M$ such that for all $f \in M_d(\bar{\mathbb{Q}}) - \{\text{Latt\`es}\}$ such... | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/1/#03c32d520917a449e9e2d9c17d004ca6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Known for Polynomial maps (Ingram).
A similar upper bound is known. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Joseph Silverman | null | null | null | [
{
"kind": "website",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.281Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9b2496e3-25ff-48d1-bfe1-9b0f54e23eb0","format_issues":null,"number":7138} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d007cdf | problem | aim-03c32d520917a449e9e2d9c17d007cdf | Equidistribution Problems | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - $f:\mathbb{P}^1 \to \mathbb{P}^1$. Is the set PCF equidistributed on $M_d$ with respect to the bifurcation measure.
- Same question for $f:\mathbb{P}^N \to \mathbb{P}^N$ with respect to **what** measure? | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d007cdf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Part (1) is known for polynomials - Thomas Gauthier and Charles Favre | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00a1ae | problem | aim-03c32d520917a449e9e2d9c17d00a1ae | Irreducibility of Gleason polynomials | {
"main": "math",
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"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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}
] | Define the Gleason polynomials as the polynomials in $c$ such that $f_c(x) = x^2+c$ is post-critically finite.
Are the Gleason polynomials irreducible? | unassessed | {
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"citation": null,
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"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00b15b | problem | aim-03c32d520917a449e9e2d9c17d00b15b | Ramfication in pre-image towers | {
"main": "math",
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"slug": "number-theory",
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"original_discipline": "mathematics"
} | [] | [
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] | There exists a finite set of primes $S$ such that all $K_n$ are unramified outside of $S$.
(Known for $\mathbb{P}^1$).
- If not PCF and $X=\mathbb{P}^1$ let $S_n = \{\text{primes of $K$ where $K_n/K$ is ramified}\}$. Is the growth rate of $\#S_n$ related to some height of $f$, specifically $\hat{h... | unassessed | {
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"citation": null,
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"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | 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"
] | Rafe Jones | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00b522 | problem | aim-03c32d520917a449e9e2d9c17d00b522 | Detecting PCF maps | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Let $f$ be a PCF rational function defined over a number field. Is it ``algebraically detectable'' from $K_n = K(\mathop{Per}_n(f))$ or the tower of such extensions that $f$ is PCF. Galois groups? Ramification? | unassessed | {
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"url": "http://aimpl.org/finitedynamics/4/#03c32d520917a449e9e2d9c17d00b522",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/4/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00c0ae | problem | aim-03c32d520917a449e9e2d9c17d00c0ae | Critical orbit relations | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | An algebraic subvariety in $M_d$ has a Zariski dense subset of PCF maps if and only if that subvariety is defined by critical orbit relations.
- Let $X \subset \mathbb{A}^2$ be a curve. Is it true that you have infinitely many points $(c_1,c_2) \in X$ such that $z^2+c_1$ and $z^2+c_2$ are both PCF if a... | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | 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"
] | Lauran DeMarco/Patrick Ingram | null | null | null | [
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"79f2c53b-706a-4526-b84e-56d2f684be94","format_issues":null,"number":7140} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00da3f | problem | aim-03c32d520917a449e9e2d9c17d00da3f | Notions of PCF | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - Does (1) imply (2)?
- Are PCF (1) or (2) Zariski dense in $M_d^N$?
- Is there are more general definition than (\ref{it1}) such that:
a) ``there are more of them''? (i.e. less restrictive)
b) they are dense in any reasonable topology
c) Andre-Oort property | unassessed | {
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"url": "http://aimpl.org/finitedynamics/5/#03c32d520917a449e9e2d9c17d00da3f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/5/",
"note": null,
"sort_order": 0
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] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"dd0e8311-baaa-4510-9692-ebb8ffdaedff","format_issues":null,"number":7151} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00e8e7 | problem | aim-03c32d520917a449e9e2d9c17d00e8e7 | PCF locus | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - How big is the PCF locus in $M_d^N$?
- Given a ``critical portrait'' when is the set of PCF maps with that portrait zero dimensional? (what are the obvious counter examples?) | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d00e8e7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/2/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.295Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b8b136a1-3e32-4092-9ece-2209928873b6","format_issues":null,"number":7141} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00fb67 | problem | aim-03c32d520917a449e9e2d9c17d00fb67 | Entropy | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - Let $f(z) = z^2 + c$, $c \in \mathbb{R}$ and PCF with invariant $[a,b]$ with fixed point at one end. Which algebraic numbers arise as $e^s$ where $s$ is the entropy of $f$?
- More generally, for $z^2+c$ on its Hubbard tree (or higher degree).
- Is there an algebraic analogue of entropy (like dyna... | unassessed | {
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"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/6/#03c32d520917a449e9e2d9c17d00fb67",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/6/",
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"sort_order": 0
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] | {
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.354Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"26b8c9ef-7bf7-4bac-adde-33e3fba8a242","format_issues":null,"number":7154} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d01077e | problem | aim-03c32d520917a449e9e2d9c17d01077e | $p$-adic PCF locus | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Is $M_d(\mathbb{Q}_p) \cap PCF$ (or polynomials $P_d(\mathbb{Q}_p) \cap PCF$) infinite for all $p$? (maybe no for $p > d$, but what about $p < d$?) What are the accumulation points? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d01077e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/2/",
"note": null,
"sort_order": 0
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"created_at": "2026-09-08T03:32:15.935Z",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"03087f97-8e30-473c-a134-59b4b5fb78aa","format_issues":null,"number":7142} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d011139 | problem | aim-03c32d520917a449e9e2d9c17d011139 | field of definition vs field of moduli | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Are all PCF maps defined over their field of moduli? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d011139",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/2/",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"30dd287c-4f05-44bf-85d8-3f7e0f3843c0","format_issues":null,"number":7143} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d012236 | problem | aim-03c32d520917a449e9e2d9c17d012236 | Algebraic proof of Thurston rigidity | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
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] | Algebraic proof of infinitesimal Thurston Rigidity, i.e. if $f$ is PCF non-Latt\`es and degree at least 2, then $1$ is not an eigenvalue of $f^{\ast}:H^1(\mathbb{P}^1,\Theta_{P_f}) \to H^1(\mathbb{P}^1,\Theta_{P_f})$ where $P_f$ is the post-critical set and $\Theta$ is the sheaf of holomorphic vector fields with zeros ... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/3/#03c32d520917a449e9e2d9c17d012236",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | 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"
] | Adam Epstein | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/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 | [
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"published_at": "2026-09-08T03:33:08.323Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0a1833f1-4653-4af2-ba15-d6f9ac2875c3","format_issues":null,"number":7147} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d0128c4 | problem | aim-03c32d520917a449e9e2d9c17d0128c4 | Milnor's Characterisation of Lattes | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - Does this hold over positive characteristic?
- What do you get from the dual of Frobenius when inseparable?
- What about characteristic 2 and 3 and $\mathop{Aut}(E)$ nonabelian? | unassessed | {
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"url": "http://aimpl.org/finitedynamics/6/#03c32d520917a449e9e2d9c17d0128c4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/6/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.358Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a7045bee-1493-4731-91f3-67bcd0ed6bf1","format_issues":null,"number":7155} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d01294e | problem | aim-03c32d520917a449e9e2d9c17d01294e | portraits of rigid Latt\es | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | What portraits occur for the rigid Latt\`es maps? In particular, are any of them the flexible Latt\`es portraits? | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/6/#03c32d520917a449e9e2d9c17d01294e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/6/",
"note": null,
"sort_order": 0
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] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.362Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c7c5609e-c8a3-4c08-9102-1349e62c4ae2","format_issues":null,"number":7156} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d013128 | problem | aim-03c32d520917a449e9e2d9c17d013128 | Classification of moduli space | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Fix $d$. If $n >>_d 1$, then is $M_d(n)$ of general type, where $M_d(n)$ marks periodic points of formal period $n$. | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d013128",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Known for abelian varieties and for $d=2$, $n=1,\ldots,5$ $M_d(n)$ is rational and $M_2(6)$ is general type (Blanc-Canci) | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Joseph Silverman | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.307Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"de1e6cfc-cfd1-4a7f-a660-4214bfbeab40","format_issues":null,"number":7144} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d013eee | problem | aim-03c32d520917a449e9e2d9c17d013eee | regular polynomial endomorphisms | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Fix $d,N$. $f:\mathbb{P}^N \to \mathbb{P}^N$ is a regular polynomial endomorphism if it leaves a hyperplane invariant, call the space of them $R_d^N$. If we restrict each $f$ to its hyperplane it gives a projection $\pi: R_d^N \to M_d^{N-1}$. In any given fiber of $\pi$ is there a curve of PCF maps? (Known: Ingram-Ther... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/2/#03c32d520917a449e9e2d9c17d013eee",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | 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"
] | Patrick Ingram | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/2/",
"note": null,
"sort_order": 0
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] | {
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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": "2026-09-08T03:33:08.313Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"221f35e3-1a3a-4886-90a3-21105ebce564","format_issues":null,"number":7145} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d014bd7 | problem | aim-03c32d520917a449e9e2d9c17d014bd7 | inertia groups for preimage towers | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | - What can you say about inertia subgroups of Galois groups in towers of fields generated by $f^{-n}(\alpha)$ for $f$ PCF?
- What happens to decomposition groups? | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/4/#03c32d520917a449e9e2d9c17d014bd7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "03c32d520917a449e9e2d9c17d014bd7",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.336Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2ecfee61-e6fa-4977-8cec-0520f020b58f","format_issues":null,"number":7150} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d014def | problem | aim-03c32d520917a449e9e2d9c17d014def | Are there any more conspiracies? | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Let $\mathop{Per}_n(\lambda)$ be the locus in the moduli space of formal $n$-cycles with multiplier $\lambda$. $\mathop{Per}_n(\lambda)$ is in general an irreducible cubic, $\\mathop{Per}_3(1)$ factors. Let $\mathop{Per}^{\ast}_n(\lambda)$ be the same but with actual $n$-cycles instead of formal $n$-cycles. $\mathop{Pe... | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/6/#03c32d520917a449e9e2d9c17d014def",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | 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"
] | Adam Epstein | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "03c32d520917a449e9e2d9c17d014def",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.367Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b724d519-759f-4682-8188-d17ef42c224d","format_issues":null,"number":7157} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d018892 | problem | aim-03c32d520917a449e9e2d9c17d018892 | Thurston Rigidity Exceptions | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | What are the ``obvious'' exception to Thurston Rigidity in $M_d^N$? | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/5/#03c32d520917a449e9e2d9c17d018892",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Postcritically finite maps in complex and arithmetic dynamics",
"url": "http://aimpl.org/finitedynamics/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "03c32d520917a449e9e2d9c17d018892",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.345Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bae8f245-350a-44df-b9ab-40ead202c80a","format_issues":null,"number":7152} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d018f0a | problem | aim-03c32d520917a449e9e2d9c17d018f0a | Flexible Family of PCF maps | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/finitedynamics/ Not an author-supplied MSC code."
}
] | Is there a flexible family of PCF maps that does not come from $\mathbb{P}^1$. | unassessed | {
"key": "aimpl",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitedynamics/5/#03c32d520917a449e9e2d9c17d018f0a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Postcritically finite maps in complex and arithmetic dynamics · Historical workshop question | ## Workshop introduction
This set of problems is the result of an open problem discussion held on the first day of this AIM workshop on post-critically finite maps in complex and arithmetic dynamics. The problems range from broad questions to specific conjectures. Several of these problems were resolved (or partially ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
resolved: yes. | null | published | incremental | hard | [
"aim",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"192d794f-06bf-4c1a-9045-699490697107","format_issues":null,"number":7153} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d01fa7c | problem | aim-03c32d520917a449e9e2d9c17d01fa7c | Estimates for $\overline{\partial}$ · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ that contains $0$ and let $\phi\in L^1_{loc}(\Omega)$ be a weight function on $\Omega$. Let $H$ be a hyperplane through $0$ and $f$ be a holomorphic function on $H\cap\Omega$ such that $$\int_{H\cap\Omega}|f|^2e^{-\phi}dV<\infty.$$
Suppose that for some constant $... | unassessed | {
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"url": "http://aimpl.org/crscv/1/#03c32d520917a449e9e2d9c17d01fa7c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Varolin | null | null | null | [
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"published_at": "2026-09-08T03:33:08.684Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ce59391b-ee68-4783-9a0b-886b4c413fee","format_issues":null,"number":7228} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d0210dd | problem | aim-03c32d520917a449e9e2d9c17d0210dd | Estimates for $\overline{\partial}$ · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\mathcal{W}$ be the smooth Diederich--Fornaess worm domain in $\mathbb{C}^2$ (see \cite{MR0430315}) and $\rho$ be a defining function for $\mathcal{W}$. Let $g_{\rho}$ be the K\"ahler metric on $\mathcal{W}$ whose K\"ahler 2-form is $i\partial\overline{\partial}\log(-\rho).$
Study the $\mathcal{C}^{\infty}$-regul... | unassessed | {
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"url": "http://aimpl.org/crscv/1/#03c32d520917a449e9e2d9c17d0210dd",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Dragomir | null | null | null | [
{
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ea81b22d-b7d9-48dc-9fc8-c10c7f73d322","format_issues":null,"number":7229} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02218f | problem | aim-03c32d520917a449e9e2d9c17d02218f | Estimates for $\overline{\partial}$ · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega$ be a smooth bounded domain in $\mathbb{C}^n$ such that the automorphism group of $\Omega$ is non-compact. What can be said about $\Omega$?
See \cite{MR1706680}. | unassessed | {
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"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Catlin | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d022abb | problem | aim-03c32d520917a449e9e2d9c17d022abb | Estimates for $\overline{\partial}$ · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\mathcal{W}$ be the smooth Diederich--Fornaess worm domain in $\mathbb{C}^2$ and $\mathbf{B}_{\mathcal{W}}$ denote the Bergman projection operator on $\mathcal{W}$. Prove or disprove that $\mathbf{B}_{\mathcal{W}}(\log \overline{z_1})$ is in $\mathcal{C}^{\infty}(\overline{\mathcal{W}})$. Note that if it fails to ... | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
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"url": "http://aimpl.org/crscv/1/#03c32d520917a449e9e2d9c17d022abb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Straube | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/1/",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"676492a1-47e2-4f7a-b6a7-8abc79dda7df","format_issues":null,"number":7231} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d022bef | problem | aim-03c32d520917a449e9e2d9c17d022bef | Estimates for $\overline{\partial}$ · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega$ be a smooth bounded pseudoconvex domain such that for any $0<\eta<1$, there exists a defining function $\rho_{\eta}$ such that $-(-\rho_{\eta})^{\eta}$ is plurisubharmonic on $\Omega$. Note that such an $\eta$ always exists \cite{MR0430315}; however, it could be small. Determine minimal assumptions on $\Om... | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/1/#03c32d520917a449e9e2d9c17d022bef",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Harrington | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/1/",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c8f1141c-7025-49a1-8a25-0846e609f02f","format_issues":null,"number":7232} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d023572 | problem | aim-03c32d520917a449e9e2d9c17d023572 | Obstruction to Compactness · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega$ be a smooth bounded pseudoconvex domain, let $\mathbf{B}_{\Omega}$ denote the Bergman projection operator and $M_{\psi}$ denote the multiplication operator by $\psi$. Suppose that $[\mathbf{B}_{\Omega},M_{\psi}]$ is compact on $L^2(\Omega)$ for all $\psi\in C(\overline{\Omega})$. Is $N_1$ compact on $L^2_{... | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/2/#03c32d520917a449e9e2d9c17d023572",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
$\bullet$ Yes, if $\Omega$ is convex \cite{MR1659575}.
$\bullet$ No, if $\Omega$ is not pseudoconvex \cite{MR3095048}. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | \c{S}ahuto\u{g}lu | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.708Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c6d8d063-4e81-4e11-b873-246875400276","format_issues":null,"number":7233} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d023f18 | problem | aim-03c32d520917a449e9e2d9c17d023f18 | Obstruction to Compactness · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\Omega_2\subset \Omega_1$ be two smooth bounded pseudoconvex domains that share a boundary point $p$. If the restriction map from $A^2(\Omega_1)$ into $A^2(\Omega_2)$ is not compact, is the D'Angelo type of $p$ the same with respect to $\Omega_1$ and $\Omega_2$?
$\bullet$ When the inside domain $\Omega_2$ is a ba... | unassessed | {
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"url": "http://aimpl.org/crscv/2/#03c32d520917a449e9e2d9c17d023f18",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | \c{S}ahuto\u{g}lu | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/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 | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"829af502-6f9b-4407-b793-466b7144b697","format_issues":null,"number":7234} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d024739 | problem | aim-03c32d520917a449e9e2d9c17d024739 | Obstruction to Compactness · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Describe the relation between compactness of the $\overline{\partial}$-Neumann operator and existence of a Stein neighborhood basis. In particular, does the geometric sufficient condition for compactness in \cite{MR2097419} imply existence of a Stein neighborhood basis? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/crscv/2/#03c32d520917a449e9e2d9c17d024739",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Straube | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/2/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.717Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d5f80ebd-6a59-481a-86c6-bc37b693115b","format_issues":null,"number":7235} |
1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d024b2a | problem | aim-03c32d520917a449e9e2d9c17d024b2a | Obstruction to Compactness · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Is there a smooth bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^n~ (n\geq 3$) that contains a non-trivial analytic disc in $b\Omega$ and yet the $\overline{\partial}$-Neumann operator $N_1$ is compact? When $n=2$, this is not possible \cite{MR2603659}. | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/2/#03c32d520917a449e9e2d9c17d024b2a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | \c{S}ahuto\u{g}lu | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/2/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.721Z",
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d025825 | problem | aim-03c32d520917a449e9e2d9c17d025825 | Mappings · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Given proper holomorphic maps $f,g: \mathbb{B}^n\to \mathbb{B}^N$, how does one show that $f$ and $g$ are not homotopic? Find homotopy invariants for proper holomorphic maps between balls.
$\bullet$ Special case (Lebl): Is the Faran map from $\mathbb{B}^2$ to $\mathbb{B}^4$ given by $$(z,w) \to (z^3,\sqrt{3}zw, w^3,0)... | unassessed | {
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The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
It is known that the Faran map is homotopic to this embedding when the target dimension is 5, and it is not homotopic when the target dimension is 3. | null | published | incremental | hard | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02591a | problem | aim-03c32d520917a449e9e2d9c17d02591a | Mappings · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $R(z,\overline{z})$ be a bihomogeneous polynomial. Find necessary and sufficient conditions such that there exists an integer $N$ with
$$(R(z,\overline{z}))^N=\sum_{j=1}^{m}|p_j(z)|^2.$$
Here $p_j(z)$'s are linearly independent holomorphic polynomials. See \cite{MR1682713} and \cite{MR2770459}. | unassessed | {
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"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | D'Angelo | null | null | null | [
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"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d025eed | problem | aim-03c32d520917a449e9e2d9c17d025eed | Mappings · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $R(z,\overline{z})$ be a Hermitian polynomial that is a sum of squares (SOS)
$$R(z,\overline{z})=\sum_{j=1}^m|p_j(z)|^2,$$
where $p_j(z)$'s are linearly independent holomorphic polynomials. Suppose that $R(z,\overline{z})$ is divisible by $||z||^2$ (i.e. $R(z,\overline{z})=||z||^2A(z,\overline{z})$). What are the ... | unassessed | {
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"url": "http://aimpl.org/crscv/3/#03c32d520917a449e9e2d9c17d025eed",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Ebenfelt | null | null | null | [
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"citation": "The Cauchy-Riemann equations in several variables",
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d026390 | problem | aim-03c32d520917a449e9e2d9c17d026390 | Mappings · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $D_1$ and $D_2$ be two bounded symmetric domains such that neither is a ball. Let $F:D_1\to D_2$ be a proper holomorphic map. Is $F$ a **trivial map**, that is $F(z)=(z,g(z))$, in suitable coordinates, where $g(z)$ is a vector valued holomorphic function? By a result of Tsai, the answer is yes when the rank (as a b... | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Zaitsev and Mok | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d026b8e | problem | aim-03c32d520917a449e9e2d9c17d026b8e | Mappings · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | It was proven by Eliashberg that any embeddable CR-structure on $\mathbb{S}^3$ bounds a Stein manifold $X\simeq \mathbb{B}^4$ with a strictly plurisubharmonic exhaustion function with a single critical point. Can $X$ always be embedded into $\mathbb{C}^2$? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/3/#03c32d520917a449e9e2d9c17d026b8e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Epstein | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02a50e | problem | aim-03c32d520917a449e9e2d9c17d02a50e | Normal Forms · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $C$ be a class of hypersurfaces defined by a finite order condition. A normal form is a subclass $C_0$ where normal representatives are determined up to a finite dimensional group. For example, for Levi non-degenerate hypersurfaces there is the Chern-Moser normal form and for finite type hypersurfaces in $\mathbb{C... | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/crscv/5/#03c32d520917a449e9e2d9c17d02a50e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Zaitsev | null | null | null | [
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"citation": "The Cauchy-Riemann equations in several variables",
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02c51e | problem | aim-03c32d520917a449e9e2d9c17d02c51e | Spectrum of $\overline{\partial}$-Neumann Laplacian · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Compute the spectrum of the $\overline{\partial}$-Neumann Laplacian on the Hartogs triangle and on the Diederich-Fornaess worm domain. In particular, determine whether or not the corresponding spectra are discrete. | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/6/#03c32d520917a449e9e2d9c17d02c51e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Fu | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/6/",
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02ca93 | problem | aim-03c32d520917a449e9e2d9c17d02ca93 | Spectrum of $\overline{\partial}$-Neumann Laplacian · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Relate the infimum of the essential spectrum of the $\overline{\partial}$-Neumann Laplacian on the worm domain to the winding of the domain. | unassessed | {
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"name": "AIM · The Cauchy-Riemann equations in several variables",
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"url": "http://aimpl.org/crscv/6/#03c32d520917a449e9e2d9c17d02ca93",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Fu | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02d378 | problem | aim-03c32d520917a449e9e2d9c17d02d378 | Spectrum of $\overline{\partial}$-Neumann Laplacian · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Is the spectrum of the $\overline{\partial}$-Neumann Laplacian on a bounded smooth pseudoconvex domain in $\mathbb{C}^n$ always discrete? Is the infimum of the spectrum always a point eigenvalue (ground state energy)? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/6/#03c32d520917a449e9e2d9c17d02d378",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Fu | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d02d5ae | problem | aim-03c32d520917a449e9e2d9c17d02d5ae | Spectrum of $\overline{\partial}$-Neumann Laplacian · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\phi:\mathbb{C}^n\to\mathbb{R}$ be a $C^2$ plurisubharmonic function. Determine the relation between the eigenvalues of the complex Hesssian of $\phi$ and the compactness of the $\overline{\partial}$-Neumann operator on $L^2_{(0,q)}(\mathbb{C}^n,e^{-\phi})$. See \cite{MR3029187} for $n=1$. Determine the relation b... | unassessed | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/6/#03c32d520917a449e9e2d9c17d02d5ae",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Prob... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Cauchy-Riemann equations in several variables · Historical workshop question | ## Workshop introduction
The Cauchy-Riemann Equations in Several Variables.
June 9 to June 13, 2014 | 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"
] | Haslinger | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/6/",
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1.0.0 | problem:aim-0c26f455c0cdf5d41cf7a7b22a00b51d | problem | aim-0c26f455c0cdf5d41cf7a7b22a00b51d | The Case $\ell_2\otimes_{\pi}\ell_2\otimes_{\pi}\ell_2$ | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/convexbanach/ Not an author-supplied MSC code."
}
] | The result of Briet, Naor and Regev does not cover the case where $p=q=r=2$ and therefore, it remains open whether $\ell_2\otimes_{\pi}\ell_2\otimes_{\pi}\ell_2$ has non-trivial cotype or not. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariants in convex geometry and Banach space theory ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/convexbanach/2/#0c26f455c0cdf5d41cf7a7b22a00b51d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariants in convex geometry and Banach space theory · AIMPL workshop record | ## Section context
A very easy fact about cotype and projective tensor spaces is that $L_1\otimes_{\pi} X$ always inherits the cotype of $X$. However, in general these questions ask for highly non-trivial methods and quite involved tools.
In 1974, Tomczak-Jaegermann proved that the projective tensor space $\ell_2\ot... | 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"
] | G. Pisier | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0c26f455c0cdf5d41cf7a7b22a00b56e | problem | aim-0c26f455c0cdf5d41cf7a7b22a00b56e | The Case $L_p\otimes_{\pi} L_q$ | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/convexbanach/ Not an author-supplied MSC code."
}
] | It is still an open question whether $L_p \otimes_{\pi} L_q$ has finite cotype for $p\in(1,2)$ and $q\in(1,2]$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariants in convex geometry and Banach space theory ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/convexbanach/2/#0c26f455c0cdf5d41cf7a7b22a00b56e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariants in convex geometry and Banach space theory · AIMPL workshop record | ## Section context
A very easy fact about cotype and projective tensor spaces is that $L_1\otimes_{\pi} X$ always inherits the cotype of $X$. However, in general these questions ask for highly non-trivial methods and quite involved tools.
In 1974, Tomczak-Jaegermann proved that the projective tensor space $\ell_2\ot... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
It is still an open question whether $L_p \otimes_{\pi} L_q$ has finite cotype for $p\in(1,2)$ and $q\in(1,2]$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | G. Pisier | null | null | null | [
{
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{
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... | {
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1.0.0 | problem:aim-0c26f455c0cdf5d41cf7a7b22a00cc2f | problem | aim-0c26f455c0cdf5d41cf7a7b22a00cc2f | Cotype of Projective Tensor Spaces · Question 2.3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/convexbanach/ Not an author-supplied MSC code."
}
] | This was a blank problem, and David added this sentence. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariants in convex geometry and Banach space theory ",
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"url": "http://aimpl.org/convexbanach/2/#0c26f455c0cdf5d41cf7a7b22a00cc2f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariants in convex geometry and Banach space theory · AIMPL workshop record | ## Section context
A very easy fact about cotype and projective tensor spaces is that $L_1\otimes_{\pi} X$ always inherits the cotype of $X$. However, in general these questions ask for highly non-trivial methods and quite involved tools.
In 1974, Tomczak-Jaegermann proved that the projective tensor space $\ell_2\ot... | 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": "Invariants in convex geometry and Banach space theory · Original question",
"url": "http://aimpl.org/convexbanach/2/#0c26f455c0cdf5d41cf7a7b22a00cc2f",
"note": null,
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{
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"3dee959b-50cc-4a4c-af83-f8d96f7ca7d0","format_issues":null,"number":11057} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e0029b0 | problem | aim-0df1011a6fa8a3c46e2c977b7e0029b0 | The Problems · Question 05 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | - (i) Let $\mathcal{P}_d := \left\{f(z)=
\sum\limits_{j=0}^{d}a_j z^j \ | \ a_j \geq 0~
\forall j, ~~f(z)=0 \implies z \in \mathbb{R}\right\}$.
Which functions $F: \mathbb{R}_+ \longrightarrow
\mathbb{R}_+$ such that $F(0)=0$ map $\mathcal{P}_d$ into
itself, where $F[f](z) :=
\sum\limits_{j=0}^{d}F(a_j)z^j... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e0029b0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Apoorva Khare, Petter Branden, ... | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.877Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"22165c46-4565-470c-9777-497bd51a5e9c","format_issues":null,"number":8694} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e0074da | problem | aim-0df1011a6fa8a3c46e2c977b7e0074da | The Problems · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Given positive scalars $a_0, \dots, a_d$ such that
$\frac{a_k^2}{a_{k-1}a_{k+1}}\geq 4$ for $0 < k < d$, Hutchinson's
theorem says that the generating polynomial $p(x) :=
\sum\limits_{j=0}^{d} a_jx^j$ is real-rooted. One can homogenize this to
$p(x,y)$.
Now consider the analogue for homogeneous polynomials of three va... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e0074da",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Petter Branden | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
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] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e0074da",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.882Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3152768c-c9ea-40a5-baf8-f96c5ad89e57","format_issues":null,"number":8695} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e008c4d | problem | aim-0df1011a6fa8a3c46e2c977b7e008c4d | The Problems · Question 15 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | The Aissen--Edrei--Schoenberg--Whitney (AESW) theorem states that
a real sequence $(a_0,a_1,a_2,\ldots)$ with $a_0 \neq 0$ is a one-sided
PF sequence $\Leftrightarrow F(z)=a_0 e^{\delta z}
\prod\limits_{j=0}^{\infty}\frac{1+\alpha_j z}{1-\beta_jz}$ for
$\alpha_j, \beta_j, \delta, a_0 \geq 0$ and $\sum_j (\alpha_j + \be... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e008c4d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Alan Sokal | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.887Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"68d98e18-67e7-4a4b-b9e8-94375251ace0","format_issues":null,"number":8696} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e008d18 | problem | aim-0df1011a6fa8a3c46e2c977b7e008d18 | The Problems · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Let
$$
M_{\bf A} :=
{\scriptsize \begin{pmatrix}
A_0 & 0 & 0 & \cdots\\
A_1 & A_0 & 0 & \cdots\\
A_2 & A_1 & A_0 & \cdots\\
\vdots & \vdots & \vdots & \ddots
\end{pmatrix}} \in TN,
$$
and $F(t)=A_0+tA_1+t^2A_2+\cdots \in M_2[[t]],$ where $A_0$ is invertible.
Is there an AESW-type factorization for $F(t)$? | unassessed | {
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"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e008d18",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Pavlo Pylyavskyy | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e008d18",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.893Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7b422276-e4b2-4f05-a436-bb012fc715a5","format_issues":null,"number":8697} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00a0d2 | problem | aim-0df1011a6fa8a3c46e2c977b7e00a0d2 | The Problems · Question 25 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Classify real linear combinations of products of minors that are
nonnegative for all $TN$ matrices. More concretely, given a
polynomial $p( \{ x_{I \times J} \ | \ I,J \subset [n], |I| = |J| \}
)$, when can one certify, via some constructive algorithmic process, that evaluating $p$ at $x_{I \times J} =
\det A_{I \t... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00a0d2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop:
## Question context
An algorithmic process is known to identify inequalities that compare the products of two minors for all $TN$ matrices. | 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"
] | Prateek Kumar Vishwakarma | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e00a0d2",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.897Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"af1e41cd-57b0-40d8-8154-672cdde1134b","format_issues":null,"number":8698} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00b681 | problem | aim-0df1011a6fa8a3c46e2c977b7e00b681 | The Problems · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider $TN$ Toeplitz matrices. What are the allowed patterns of
zero and nonzero minors (i.e., which positroid cells contain
Toeplitz matrices)? How does this relate to P\'olya frequency
sequences? (Check work by Rietsch for the lower triangular
Toeplitz case.)
Is it enough to check all the corner minors to iden... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00b681",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Melissa Sherman-Bennett | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:15.902Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48f51c6a-0282-4528-ae2e-415043f848d4","format_issues":null,"number":8699} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00ba4d | problem | aim-0df1011a6fa8a3c46e2c977b7e00ba4d | The Problems · Question 35 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider semi-infinite lower triangular $TN$ Toeplitz matrices. Under what conditions can a non-trivial $k\times k$ minor be zero? | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
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"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00ba4d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Alan Sokal, ... | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.906Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3bada86d-bf48-48bd-8875-39adb658d7ab","format_issues":null,"number":8700} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00cd5c | problem | aim-0df1011a6fa8a3c46e2c977b7e00cd5c | The Problems · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | There are many classical theorems about operations that preserve
negative-real-rootedness of polynomials: for instance, $d/dx + a$
or $x \cdot d/dx + a$ with $a \ge 0$; or Hadamard product; or Hadamard
product with an extra $n!$ (sometimes known as Schur composition);
or Br\"and\'en's (2011) log-concavity operation $... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00cd5c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Robert Angarone, Alan Sokal | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.911Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"993a5a35-3dcb-4999-a965-6ba18e88dffe","format_issues":null,"number":8701} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00d4f7 | problem | aim-0df1011a6fa8a3c46e2c977b7e00d4f7 | The Problems · Question 45 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | It was recently shown that if $\lambda, \mu$ are $N$-tuples of
positive integers, then the ratio of Schur polynomials $s_\lambda
/ s_\mu$, when evaluated at $N$ real variables with values in
$(0,1]^N$ (the ``log-negative orthant''), is minimized at
$(1,\dots,1)$ if and only if $-\lambda$ weakly majorizes $-\mu$.
... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00d4f7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Apoorva Khare, Alan Sokal | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.915Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bc28a2ae-d764-4751-b9ab-7a1f62f29f91","format_issues":null,"number":8702} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00dfa2 | problem | aim-0df1011a6fa8a3c46e2c977b7e00dfa2 | The Problems · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider a bipartite graph $G$ on an annulus, with a fixed
``base'' perfect matching $\mu$. Given any other $\mu'$,
superimpose it on $\mu$; this gives a bunch of cycles. Count the
number of non-contractible cycles $=f(\mu')$. Running over all
$\mu' \neq \mu$, we get
$$ \sum_{k \geq 0} \
\sum_{\mu'\neq \mu \ | \ ... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00dfa2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Pavlo Pylyavskyy | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present",
"known-source-format-issue"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.920Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c4dd5b19-168e-489b-9edd-f3305fd479ce","format_issues":{"errors":1,"fields":["statement"]},"number":8703} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00e659 | problem | aim-0df1011a6fa8a3c46e2c977b7e00e659 | The Problems · Question 55 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $n,r \geq 1$ are integers, and $(\lambda_1, \dots,
\lambda_r)$ and $(\mu_1, \dots, \mu_r)$ are (non-increasing)
partitions of $n$. If $\mu$ majorizes $\lambda$, then for
all $TN$ matrices $A$ we have:
$$
\lambda_1! \cdots \lambda_r! \sum_I \prod_{k=1}^r \det A_{I_k
\times I_k} \geq
\mu_1! \cdots \mu_r!... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00e659",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This has now been answered affirmatively. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Apoorva Khare | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.924Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b3e2d8d6-f6a8-43e5-b031-996d99f0d9e4","format_issues":null,"number":8704} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00ec52 | problem | aim-0df1011a6fa8a3c46e2c977b7e00ec52 | The Problems · Question 6 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is Fisk's conjecture true for $3 \times 3$ minors / $n \times n$
minors? Namely, if $\sum_{k=0}^d a_k z^k$ is a real-rooted
polynomial with all $a_k > 0$, then Br\"and\'en showed the ``$2
\times 2$ analogue'':
$$
\sum_{k \geq 0} \left| \begin{matrix} a_k & a_{k-1} \\ a_{k+1} &
a_k \end{matrix} \right| z^k
$$
... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00ec52",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | 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"
] | Petter Branden | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e00ec52",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.928Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b9a1e615-a6f3-4feb-a9a3-25a823ef8dc0","format_issues":null,"number":8705} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e00fc03 | problem | aim-0df1011a6fa8a3c46e2c977b7e00fc03 | The Problems · Question 65 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\lambda \geq 4$. Given a (strictly) ${TP}_1$ square matrix
$A$, it is known that if $ad - \lambda bc > 0$ for every $2 \times 2$ submatrix
$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ of $A$, then $A$
is (strictly) TP.
The question is if this fact can be extended to higher orders of
total positivity. N... | unassessed | {
"key": "aimpl",
"name": "AIM · Theory and applications of total positivity",
"type": "workshop-problem-list",
"url": "http://aimpl.org/totalpos/1/#0df1011a6fa8a3c46e2c977b7e00fc03",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Theory and applications of total positivity · Historical workshop question | ## Section context
The following problems raised/discussed during the workshop: | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A quantitative condition in $\lambda$ has been formulated and shown to be sufficient; it is not clear if the value of $\lambda$ is tight. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Charles Johnson, Steven Karp | null | null | null | [
{
"kind": "website",
"citation": "Theory and applications of total positivity",
"url": "http://aimpl.org/totalpos/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e00fc03",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.933Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c64bf69b-2443-4e93-9c5e-c886ddd336e4","format_issues":null,"number":8706} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02b43d | problem | aim-0df1011a6fa8a3c46e2c977b7e02b43d | Khovanov-Rozansky homology · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is the Khovanov-Rozansky homology functorial? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/2/#0df1011a6fa8a3c46e2c977b7e02b43d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e02b43d",
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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": "2026-09-08T03:33:09.041Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8ba9e27a-ba18-487e-a8e0-110cbd5363ee","format_issues":null,"number":7306} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02c41a | problem | aim-0df1011a6fa8a3c46e2c977b7e02c41a | Macdonald polynomials · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What are Schur expansions of projector closures at the category level and what are their connections to Macdonald theory? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/5/#0df1011a6fa8a3c46e2c977b7e02c41a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/5/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.099Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7bf9349b-3fb8-434b-824a-ce60f9f00809","format_issues":null,"number":7320} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02ca39 | problem | aim-0df1011a6fa8a3c46e2c977b7e02ca39 | Macdonald polynomials · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Categorify the modified Macdonald polynomials $\tilde{H_\mu}$. | unassessed | {
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The source supplies no status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02d97b | problem | aim-0df1011a6fa8a3c46e2c977b7e02d97b | Hilbert schemes · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Fixing a slope, what corresponds to a stable basis in $K$-theory of Hilbert schemes in the cocenter of the Hecke algebra? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/4/#0df1011a6fa8a3c46e2c977b7e02d97b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02e5a9 | problem | aim-0df1011a6fa8a3c46e2c977b7e02e5a9 | Hilbert schemes · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute endomorphism algebra (in the homotopy category) of projectors, and relate it to coordinate ring and of charts on Hilb$^n(\mathbb{C}^2)$ | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/4/#0df1011a6fa8a3c46e2c977b7e02e5a9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/4/",
"note": null,
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] | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e02f337 | problem | aim-0df1011a6fa8a3c46e2c977b7e02f337 | Miscellaneous · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What is the action of the full twist on the trace of the Hecke category? Does it relate to $\nabla$? How does it act on Schur objects? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/9/#0df1011a6fa8a3c46e2c977b7e02f337",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/9/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e0309b4 | problem | aim-0df1011a6fa8a3c46e2c977b7e0309b4 | Miscellaneous · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Let $B_w\in$ SBim$_n$ be the indecomposable Soergel bimodule associated to $w\in S_n$. Compute Ext$_{R-R \text{ bimod}}(B_v,B_w)$ and develop its diagrammatics. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/9/#0df1011a6fa8a3c46e2c977b7e0309b4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/9/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0ea23ebe-61ce-4d68-bba4-84337740e8a7","format_issues":null,"number":7338} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03182b | problem | aim-0df1011a6fa8a3c46e2c977b7e03182b | Khovanov-Rozansky homology · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | If $w^2=1$, we have a map $B_w\rightarrow R$. Is the induced map $HH(B_w)\rightarrow HH(R)$ injective? Given that the Hochschild homology is defined as $HH(\beta):=\text{Ext}_{R-\text{ bimod}}(R,B)$. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/2/#0df1011a6fa8a3c46e2c977b7e03182b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e03182b",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"published_at": "2026-09-08T03:33:09.045Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dca4fa83-bfa9-4338-acda-e2f78c31df08","format_issues":null,"number":7307} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e032187 | problem | aim-0df1011a6fa8a3c46e2c977b7e032187 | Macdonald polynomials · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Let $P\in SYT(\lambda)$, $Q\in SYT(\mu)$ relate $Hom(tr(P),tr(Q))$ to the Macdonald inner product. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/5/#0df1011a6fa8a3c46e2c977b7e032187",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/5/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.108Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f285fd9a-58bf-43f0-b3f9-e5b7d88de0ea","format_issues":null,"number":7322} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e033211 | problem | aim-0df1011a6fa8a3c46e2c977b7e033211 | Khovanov-Rozansky homology · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute the Khovanov-Rozansky homology $HHH$ of cables of torus knots and develop a recursion for this class of knots. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/2/#0df1011a6fa8a3c46e2c977b7e033211",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e033211",
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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",
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.050Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ddf67c02-100a-4d79-b056-798d9f163f98","format_issues":null,"number":7308} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e033683 | problem | aim-0df1011a6fa8a3c46e2c977b7e033683 | Khovanov homology · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute the Khovanov homology of torus links. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/3/#0df1011a6fa8a3c46e2c977b7e033683",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/3/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.062Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"527e8e73-3fd0-4278-94fe-5672bc435225","format_issues":null,"number":7311} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e033c9d | problem | aim-0df1011a6fa8a3c46e2c977b7e033c9d | Macdonald polynomials · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Find the Macdonald/Schur expansion of the $a$-graded Frobenius character of the parking function space. How does the $tr(T(m,n)$ relate to the parking function module? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/5/#0df1011a6fa8a3c46e2c977b7e033c9d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/5/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.112Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c5e6d4ce-93ac-4a04-8148-241c45324e7d","format_issues":null,"number":7323} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e034b12 | problem | aim-0df1011a6fa8a3c46e2c977b7e034b12 | Hilbert schemes · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Relate $tr(T(m,n))$ to rings of quasi-invariants and to A. Wilson's conjecture. Describe $H^*(\text{Hilb}(x^{nd}=y^n))$ as a module over rational Double Affine Hecke algebra (DAHA) and relate it to the above. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/4/#0df1011a6fa8a3c46e2c977b7e034b12",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/4/",
"note": null,
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] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"038cdf6b-27f5-4f7c-992a-c3962e48d18a","format_issues":null,"number":7316} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e034d30 | problem | aim-0df1011a6fa8a3c46e2c977b7e034d30 | Khovanov-Rozansky homology · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute $HHH(JM_1^{t_1}\dots JM_n^{t_n})$ "for as many $t$'s as possible" is it parity? Describe it as an $R$-module. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/2/#0df1011a6fa8a3c46e2c977b7e034d30",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e034d30",
"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": "2026-09-08T03:33:09.054Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4450da8e-cfc3-4297-baba-96c5e9468e80","format_issues":null,"number":7309} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e035440 | problem | aim-0df1011a6fa8a3c46e2c977b7e035440 | Khovanov homology · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute $JM_1^{t_1}\dots JM_n^{t_n}$ for Khovanov homology. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/3/#0df1011a6fa8a3c46e2c977b7e035440",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/3/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.066Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"92ac367c-c2e6-4fa9-a105-eba3a3ef5913","format_issues":null,"number":7312} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e035608 | problem | aim-0df1011a6fa8a3c46e2c977b7e035608 | Braid varieties · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Develop singular braid varieties and relate them to Richardson varieties in $G/P$ and to colored homology. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e035608",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e035608",
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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": "2026-09-08T03:33:09.119Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e7306f7c-ffba-47f7-98d6-d9e164f5ec27","format_issues":null,"number":7324} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e035641 | problem | aim-0df1011a6fa8a3c46e2c977b7e035641 | Braid varieties · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What properties of braid varieties in $G/B$ should survive in $G/P$? In other words, what properties of full flag varieties remain in partial flag varieties. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e035641",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e035641",
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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": "2026-09-08T03:33:09.123Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e4efb513-a97b-4b46-bc63-7dced36a0304","format_issues":null,"number":7325} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e035d24 | problem | aim-0df1011a6fa8a3c46e2c977b7e035d24 | Braid varieties · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What is the relation between braid varieties and singular braid varieties? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e035d24",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.127Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"83cb009d-dc9c-4ed0-b82b-ac3632ff7685","format_issues":null,"number":7326} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03630c | problem | aim-0df1011a6fa8a3c46e2c977b7e03630c | Braid varieties · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Compute $H^*_T(X(\sigma_1\dots\sigma_{n-1})^m\Delta)$. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e03630c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e03630c",
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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": "2026-09-08T03:33:09.132Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"597203a1-eead-472c-ba46-ab6660a93761","format_issues":null,"number":7327} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e036bfd | problem | aim-0df1011a6fa8a3c46e2c977b7e036bfd | Braid varieties · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Are there "braid variety analogues" of projectors? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e036bfd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e036bfd",
"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": "2026-09-08T03:33:09.136Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"95378349-38cb-4964-84db-2621a8681d0b","format_issues":null,"number":7328} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e038319 | problem | aim-0df1011a6fa8a3c46e2c977b7e038319 | Braid varieties · Question 6 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Can we determine $gl(m|n)$ / Khovanov homology using braid-like varieties? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/6/#0df1011a6fa8a3c46e2c977b7e038319",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e038319",
"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": "2026-09-08T03:33:09.140Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"59134d73-615c-4f11-8bdf-507bdb9cb4e8","format_issues":null,"number":7329} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e0389b1 | problem | aim-0df1011a6fa8a3c46e2c977b7e0389b1 | Miscellaneous · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Find functors from derived horizontal trace computing $\mathcal{gl}(m|n)$-homology. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/9/#0df1011a6fa8a3c46e2c977b7e0389b1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e0389b1",
"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": "2026-09-08T03:33:09.182Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6fb20c0e-9ef8-4324-a995-24a9cf157b4c","format_issues":null,"number":7339} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e038c94 | problem | aim-0df1011a6fa8a3c46e2c977b7e038c94 | Link homology · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Make $gl(1|1)$-homology concrete and relate it to knot/tangle Floer homology. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/1/#0df1011a6fa8a3c46e2c977b7e038c94",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e038c94",
"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": "2026-09-08T03:33:09.020Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2a15c20d-0b35-44ac-b622-17834905d03a","format_issues":null,"number":7301} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e038df6 | problem | aim-0df1011a6fa8a3c46e2c977b7e038df6 | Khovanov homology · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | For Khovanov homology develop analogues of
[label=\alph*)]
- The Oblomkov-Rasmussen-Shende conjecture.
- Braid varieties.
- Hilb$^n(\mathbb{C}^2)$ should be Hilb$^n(x^2=0)$. | unassessed | {
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"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d43745cc-c4b5-43f7-8168-72a401a28464","format_issues":null,"number":7313} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e039c24 | problem | aim-0df1011a6fa8a3c46e2c977b7e039c24 | Hilbert schemes · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Relate Hilb$^n(x^2=0)$ to $HH$ of the arc algebra. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/4/#0df1011a6fa8a3c46e2c977b7e039c24",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | ## Question context
We define Hilb$^n(x^2=0)=\{\text{codiminsional }n \text{ ideals in }\mathbb{C}[x,y]/(x^2=0)\}\subseteq$ Hilb$^n(\mathbb{C}^2)$ | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/4/",
"note": null,
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"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": "2026-09-08T03:33:09.087Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"677ee1cf-c063-4890-860b-ef858d205aea","format_issues":null,"number":7317} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03b8d5 | problem | aim-0df1011a6fa8a3c46e2c977b7e03b8d5 | Hilbert schemes · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Let $\mathcal{F}(\beta)$ be the sheaf on Hilb$^n(\mathbb{C}^2)$ associated to $\beta$. How does $\mathcal{F}(\beta)|_{\text{Hilb}^n(x^2=0)}$ relate to Khovanov homology of $\beta$? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/4/#0df1011a6fa8a3c46e2c977b7e03b8d5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e03b8d5",
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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": "2026-09-08T03:33:09.091Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ea2bb8a5-0e15-43c8-9e6b-18e8a2fd0e3b","format_issues":null,"number":7318} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03c7b2 | problem | aim-0df1011a6fa8a3c46e2c977b7e03c7b2 | Link homology · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Does the superspace coinvariant ring defined as $$\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]\,\big/\,(\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]^{S_n}_+)$$ relate to link homology? What object does $$\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots,\theta_n]\,\big/\,(\mathbb{C}[x_1,\ldots,x_n,\theta_1,\ldots... | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/1/#0df1011a6fa8a3c46e2c977b7e03c7b2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e03c7b2",
"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": "2026-09-08T03:33:09.024Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5ec1b1b1-0b19-4c04-9c64-cf782191c575","format_issues":null,"number":7302} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03d6af | problem | aim-0df1011a6fa8a3c46e2c977b7e03d6af | Link homology · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Do $d$-agonal coinvariants relate to link homology? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/1/#0df1011a6fa8a3c46e2c977b7e03d6af",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e03d6af",
"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"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.029Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ffabce74-9cb3-4896-ad73-ab61a7f5c695","format_issues":null,"number":7303} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e03e21d | problem | aim-0df1011a6fa8a3c46e2c977b7e03e21d | Link homology · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Do Haiman's polygraph rings relate to link homology? How do they relate to cables of Hopf link? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebra, geometry, and combinatorics of link homology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/agclinkhom/1/#0df1011a6fa8a3c46e2c977b7e03e21d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"note... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebra, geometry, and combinatorics of link homology · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Algebra, geometry, and combinatorics of link homology",
"url": "http://aimpl.org/agclinkhom/1/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.032Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"bd751d56-d897-42e2-ba1c-d02a3c3d03c1","format_issues":null,"number":7304} |
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