OpenFrontiers
Collection
Collection of open frontier research problems. • 3 items • Updated
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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,
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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
}
] | {
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"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
}
] | {
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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
}
] | {
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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": "2026-09-08T04:58:00.456Z",
"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
}
] | {
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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": "2026-09-08T04:58:00.419Z",
"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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"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
}
] | {
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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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} | 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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"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":"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 | [
"current-status-unassessed"
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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"
] | [] | {
"created_at": "2026-09-08T04:57:39.703Z",
"updated_at": "2026-09-08T04:57:39.703Z",
"published_at": "2026-09-08T04:58:00.442Z",
"solved_at": null
} | 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 | [
"current-status-unassessed"
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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,
"note": null,
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] | {
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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,
"sort_order": 0
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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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"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": "2026-09-08T03:33:08.276Z",
"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 | [
"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": "2026-09-08T03:33:08.281Z",
"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",
"sub": "number theory",
"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"
] | null | null | null | null | [
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1.0.0 | problem:aim-03c32d520917a449e9e2d9c17d00b15b | problem | aim-03c32d520917a449e9e2d9c17d00b15b | Ramfication in pre-image towers | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"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 | {
"key": "aimpl",
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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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"published_at": "2026-09-08T03:33:08.340Z",
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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",
"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"type": "workshop-problem-list",
"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/",
"note": null,
"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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"name": "AIM · Postcritically finite maps in complex and arithmetic dynamics",
"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",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fdff2bf1-43f0-4868-8d83-e5ffb222a6ac","format_issues":null,"number":7236} |
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 | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/3/#03c32d520917a449e9e2d9c17d025825",
"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
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 | [
"aim",
"historical-workshop"
] | D'Angelo | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "03c32d520917a449e9e2d9c17d025825",
"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": "2026-09-08T03:33:08.726Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"017d0dc7-8bed-4881-b442-b7eb4662f2e7","format_issues":null,"number":7237} |
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 | {
"key": "aimpl",
"name": "AIM · The Cauchy-Riemann equations in several variables",
"type": "workshop-problem-list",
"url": "http://aimpl.org/crscv/3/#03c32d520917a449e9e2d9c17d02591a",
"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"
] | D'Angelo | null | null | null | [
{
"kind": "website",
"citation": "The Cauchy-Riemann equations in several variables",
"url": "http://aimpl.org/crscv/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "03c32d520917a449e9e2d9c17d02591a",
"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": "2026-09-08T03:33:08.730Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9bc6b7ff-d2d7-4683-a0cd-224c7e13c904","format_issues":null,"number":7238} |
End of preview. Expand in Data Studio
OpenFrontiers: research-problem corpus
A structured snapshot of the OpenFrontiers research-problem index, including mathematical and scientific problem statements, source attribution, MSC 2020 mappings, collected Lean 4 material and research-status evidence. The exact snapshot date, counts and coverage are in statistics.json.
The Lean-stated evaluation benchmark built from this corpus is released separately as OpenFrontiers-Bench (200 items) and its evaluated subset OpenFrontiers-HQ50.
The default problems configuration contains every published problem in the database,
including solved, disputed and status-unassessed records. It is not a claim that
every row is currently an unsolved problem, nor a complete census of any discipline.
One row corresponds to one indexed problem record; a paper can contain multiple
subquestions in the same record. Overlapping formulations from different sources
are retained with their own provenance. Unique IDs do not imply mathematical deduplication.
catalogues retains source problem-number indices, workshop lists, document listings,
journals and archived redirects. These rows have problem_statement: null; they are
not additional extracted problems. linked_problem_ids connects a catalogue entry
to an indexed problem. Different catalogues may point to the same item.
archive retains nonpublished historical research records separately. all_records
combines these three disjoint row sets with exactly the same schema.
train is a Hugging Face storage split name only. No train/test separation or
evaluation-contamination control has been performed.
Load
Install the versions in requirements.txt. From the dataset directory:
from datasets import load_dataset
# Reads the configurations in this dataset card.
ds = load_dataset(".", name="problems", split="train")
row = ds[0] # a Python dictionary, including nested dictionaries and lists
# Explicit file loading is also supported.
ds = load_dataset("parquet", data_files="data/problems.parquet", split="train")
math = ds.filter(lambda r: r["field"]["main"] == "math")
open_math = math.filter(lambda r: r["status"] == "open")
# From the Hugging Face Hub:
ds = load_dataset("FlippyDora/OpenFrontiers", name="problems", split="train")
The equivalent JSONL files have one JSON dictionary per UTF-8 line. Use the supplied loader for exact string preservation and explicit nullable types:
from load_jsonl import load_jsonl
ds = load_jsonl("data/problems.jsonl")
The helper uses json.loads and Dataset.from_generator with features.json.
This avoids the generic JSON loader's automatic date inference before string
casting (observed with the pinned version), which can change 2026-09-08 into
2026-09-08 00:00:00. Standard Python json.loads also reads the JSONL verbatim.
The default Parquet configurations preserve these strings without a custom loader.
These formats and configurations follow the official Hugging Face loading documentation and dataset configuration documentation.
Dictionary fields
All rows have all keys. Unknown scalar values are JSON null / Python None;
empty lists mean no collected items. Missing data is not converted into invented
statements or proofs. schema.json defines every key and type;
features.json defines the matching Hugging Face schema.
| Field | Meaning |
|---|---|
id, record_kind, slug, title |
Stable namespaced identifier, row type and problem identity. |
field.main, field.sub |
Broad discipline and subject, e.g. math, number theory. Original field name, slug and discipline are also retained. |
additional_fields |
Additional subject mappings without duplicating the primary field. |
msc2020 |
MSC codes plus mapping basis and evidence. Editorial/inferred mappings are distinguished from source mappings. A missing narrow code is not invented. |
problem_statement |
Existing Markdown/LaTeX statement, preserved verbatim. May be a summary or excerpt; see provenance. |
status |
Existing editorial status: open, unassessed, partially-solved, solved, disputed, withdrawn. Catalogue status can also include source review labels. |
source |
Collection key, source title/type/URL/citation/DOI/arXiv ID, recorded license wording and notes. |
lean4_statement |
Existing Lean 4 material, or the first deterministic linked upstream source file when the database has no Lean attachment. Can be a fragment, a whole file, or a proposition definition. |
proof, proof_status |
Accepted full-solution submission text if collected; otherwise null / not-recorded. Acceptance is editorial, not mathematical certification. |
lean4_proof, lean4_proof_status |
An accepted solution's existing verified proof, bound to the current stored target and known verification profile; otherwise null / not-recorded. |
lean4_target |
Separately stored target proposition, if available. |
formalizations |
Every collected attachment/linked Lean file, with code, language, hash, source URL, license, toolchain/commit where known, lexical placeholder flags and verification/correspondence status. |
contributions |
Collected submissions, public comments and public AI attempts. Rejected/partial/unverified attempts remain contributions rather than canonical proofs. |
teaser, background, partial_results, why_it_matters |
Existing contextual research text, preserved verbatim. |
references |
All collected citations, links, notes and original ordering. |
provenance, source_status_json |
Import/status dates, original record IDs and evidence; dated upstream status claims remain separate from local verification. |
review_state, horizon, difficulty, tags |
Original editorial/research labels; not a benchmark difficulty scale. |
posed_by, posed_year, prize_amount_usd, prize_sponsor |
Existing historical information; no fresh financial or historical verification. |
quality_flags, linked_problem_ids |
Missing full text, known formula issues, unverified source claims, source-file enrichment and catalogue links. |
dates, snapshot_at |
Stored record dates and dataset snapshot timestamp in ISO format. |
metadata_json |
JSON-encoded ancillary metadata. Catalogue rows retain their original index metadata; problem rows retain their original database ID/number and format-audit details. |
Formal statements and proofs
FormalConjectures source files are retained at the pinned commit recorded in
statistics.json; their own Lean toolchain and dependency manifest are in metadata/.
The full upstream repository is required to compile source files with their imports.
Those files can contain multiple conjectures, solved helper lemmas, answer(sorry),
or admitted declarations. A file's presence does not establish a proof of the
associated natural-language problem. All variants are preserved in formalizations.
This export does not execute Lean. Lexical sorry/admit/axiom flags mask nested
comments and strings, but are not a Lean parser or proof checker. Old source-side
"verified" labels are retained as claims in source_status_json, not promoted to
locally verified proofs. If a source reports a proof whose text was not collected,
the text remains null and a quality flag records that gap.
For any existing local verification receipt, the exporter requires the known
lean4-core-4.19.0-v1 profile, matching target and proof content hashes, a current
matching target, and an explicit axiom list contained in propext, Classical.choice,
Quot.sound. Only accepted full-solution submissions can populate canonical proof
fields. Even verified-target-only does not certify correspondence between the
Lean target and the natural-language problem. Multiple attempts remain available
in contributions; when multiple qualifying solutions exist, the most recently
created qualifying submission is selected deterministically.
Collection, coverage and limitations
The export uses a repeatable-read, read-only database snapshot plus existing source catalogues and pinned source artifacts. It preserves the corpus, rather than silently dropping uncertain or older records. No new open-problem status review is implied by export time. The metadata folder preserves source registries, selection decisions, import manifests, MSC taxonomy, review evidence and known format issues. Source catalogues are partial and differ in scope.
The sources include ICM Conjectures, COLT, TheoremDB, AIM Problem Lists, Erdős Problems,
Clay, Wikipedia subject lists, specialist collections and selected journal/workshop
articles. Source descriptions and license wording appear in metadata/sources.json.
These are not rankings or endorsements. Some inherited records are summaries rather
than complete standalone formulations; provenance.has_full_text and quality flags
make recorded gaps filterable. Source-reported solved or open status can be outdated.
Markdown/LaTeX and Unicode are preserved, including known upstream formatting
problems rather than silently rewriting mathematics. Site-relative figure/document
links remain verbatim; metadata/asset-manifest.json records referenced assets and
metadata/aim-documents.json maps cached AIM documents to original URLs. Binary PDFs
and figures are not bundled in this text dataset. Some records therefore require
the cited source for figures or complete context.
Operational accounts, sessions, credentials, private AI prompts, private attempts, payments and usage logs are outside the research-data export. Public research authorship/citations are retained. There are no inferred demographic annotations.
Reuse and upload
This is a mixed-source dataset, not a blanket CC0/Apache-licensed corpus.
See NOTICE.md, each row's source.license, attachment licenses and
original source notices. Technical upload readiness does not establish unrestricted
redistribution or training rights for every source. The dataset preserves all
existing research records so downstream users can apply source-specific policies.
Authenticate using the Hugging Face CLI, then preview the upload file list:
hf auth login
python upload.py --repo-id OWNER/DATASET
# When ready, this creates/updates a private dataset repository:
python upload.py --repo-id OWNER/DATASET --upload
# To choose public visibility when creating a NEW repository, also pass --public.
The upload helper checks checksums.sha256 and the successful validation report
before sending files. No upload occurs without --upload. Existing repository
visibility is not changed by this helper. Uploading does not delete older remote
files, so a new versioned repository is the simplest way to publish an exact snapshot.
Reproducibility and validation
input-manifest.json records input hashes. validation.json records the completed
schema, count, reference, content-preservation and JSONL/Parquet/Hugging Face loading
checks. checksums.sha256 covers all packaged files except itself. Export scripts
and pinned dependencies are in reproduce/. Archived TypeScript scripts use
.ts.txt names so this package does not alter the application's build; restore
their .ts extension under scripts/dataset/ in the application repository to run them.
To rebuild from the application repository, first stop its preview if it shares
the embedded database, then take a read-only research snapshot (or use a fully
offline database copy through PGLITE_DATA_DIR). Restart the preview afterward.
Never open the embedded database from two processes at once.
node --import tsx scripts/dataset/snapshot.ts .tmp/hf-dataset-snapshot.json
python scripts/dataset/export.py --snapshot .tmp/hf-dataset-snapshot.json \
--formal-root PATH/TO/PINNED/formal-conjectures-COMMIT \
--theorem-snapshot PATH/TO/theorem-all.json --output datasets/NEW-VERSION
python scripts/dataset/verify.py --snapshot .tmp/hf-dataset-snapshot.json \
--dataset datasets/NEW-VERSION
Inputs must be the matching saved versions, not a fresh download at a moving branch. The raw application database and source-account API responses are not included in the upload package. JSONL and Parquet data rows can be checked independently without those private operational inputs.
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