id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
801,070 | AMR-152-0022 | Henon Maps: Open Problems — Question 22 | If $f$ is quasi-hyperbolic and dissipative, and if $J$ is connected, do the external rays land at $J$? Is $J$ a finite quotient of the real solenoid? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 22
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
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"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,071 | AMR-152-0023 | Henon Maps: Open Problems — Question 23 | Let us now suppose that $f$ is a real surface automorphism. In other words, we suppose $X$ to be projective and defined by real polynomial equations,
and $f$ to be also defined over the real numbers.
We may thus consider the restriction map $f_\mathbb{R}$ to the set of real points $X_\mathbb{R}$.
Observe that $h_{\math... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 23
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
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"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,072 | AMR-152-0024 | Henon Maps: Open Problems — Conjecture 24 | where $(c, b)\in\mathbb{C}^2$ is a parameter. (We include the case $b=0$ to simplify the presentation.) Let $J_{c, b}$ be the Julia set of $f_{c, b}$: by definition this
is the intersection between the boundaries of the sets of points having bounded forward (resp. backward) orbits.
By extension, we let $J_{c, 0}$ be th... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Conjecture 24
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,073 | AMR-152-0025 | Henon Maps: Open Problems — Question 25 | of the fundamental group of $\mathcal{H}_{\mathbb{C}}$ (with the base-point at $(c, b)=(-4, 0)$) to the group of shift-commuting automorphisms of $\{0, 1\}^{\mathbb{Z}}$ is surjective (see, e.g., [A,BS1]).
Is the locus $\mathcal{H}_{\mathbb{C}}$ connected? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 25
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,074 | AMR-152-0026 | Henon Maps: Open Problems — Question 26 (van Strien [vanstrien]) | In a topological term, monotonicity of the topological entropy of the real H\'enon map $f_{c, b}|_{\mathbb{R}^2}$ can be formulated as
Is the isentrope $\mathcal{E}_{\alpha}$ connected for any $0\leq \alpha \leq \log 2$ ? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 26
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: van Strien [vanstrien] | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,075 | AMR-152-0027 | Henon Maps: Open Problems — Question 27 | Several articles attempt at giving lower bounds for topological entropy of real H\'enon maps, e.g., [NBGM,NP]. Among others, the paper [NBGM] rigorously showed that $h_{\mathrm{top}}(f_{c, b}|_{\mathbb{R}^2})>0.46469$ for the classical H\'enon's parameter, and this bound is believed to be close to optimal. For upper bo... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 27
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,076 | AMR-152-0028 | Henon Maps: Open Problems — Question 28 | Give an asymptotic expansion of the Hausdorff dimension of $J^+_{a,c}$ as $(a,c)$ tends to $(0, 0)$. In particular is there a uniform lower bound of $\dim(J^+_{a,c})$ of the form $\dim(J^+_{a,c})\geq 3+h(a)$ with $h(a)>0$ in the neighborhood of $c=0$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 28
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,077 | AMR-152-0029 | Henon Maps: Open Problems — Question 29 | Is it possible to find a generalized complex H\'enon map $f$,
an open set $U\subset \mathbb{C}^2$ intersecting $J^+$ and a holomorphic foliation of $U$ such that
$J^+\cap U$ is a union of leaves of this foliation? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 29
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,078 | AMR-152-0030 | Henon Maps: Open Problems — Question 30 | Under which circumstances is it possible that there exist saddle points $p$ and $q$, and relative
open subsets $U\subset W^u(p)$ and $V\subset W^u(q)$
such that $U\cap K^+$ is biholomorphic to $V\cap K^+$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 30
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,079 | AMR-152-0031 | Henon Maps: Open Problems — Question 31 | Let $f_1$, $f_2$ be two generalized H\'enon maps. Under which circumstances is it possible
that some local unstable slice of $f_1$ (i.e., a set of the form $K^+\cap U$, where $U$ is a relatively
open subset of an unstable manifold)
is biholomorphically equivalent to an unstable slice of $f_2$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 31
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,080 | AMR-152-0032 | Henon Maps: Open Problems — Question 32 | Since a local unstable slice of a generalized H\'enon maps contains
essentially a complete
information about unstable multipliers, the previous question is reminiscent of the classical
``spectral rigidity'' problem:
To which extent is a generalized H\'enon map determined by the list of its unstable multipliers (resp. ... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 32
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,081 | AMR-152-0033 | Henon Maps: Open Problems — Problem 33 | Prove the existence and the uniqueness of
the equilibrium state $\mu_\phi$
associated to any
sufficiently regular weight
$\phi$
(for instance, every H\"older continuous $\phi$,
and possibly with some bound on $\max \phi - \min \phi$). | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
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"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,082 | AMR-152-0034 | Henon Maps: Open Problems — Question 34 | Suppose $\phi$ is sufficiently regular, so that
the equilibrium state $\mu_\phi$ exists and is unique.
Is it true that
\begin{equation}
\frac{1}{e^{n P(\phi)}} \sum_{x \in SP_n} e^{S_n (\phi)} \delta_x \to \mu_\phi \quad ?
\end{equation} | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 34
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,083 | AMR-152-0035 | Henon Maps: Open Problems — Problem 35 | Show that $\mu_\phi$ satisfies the CLT for H\"older continuous observables. Namely, prove that, for any H\"older continuous observable $g$, there exists $\sigma \geq 0$ such that for any interval $I \subset \mathbb{R}$, we have
\[
\lim_{n\to \infty} \mu_\phi \left(\left\{
\frac{S_n (g) - n\langle \mu_\phi,g\rangle }{\s... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,084 | AMR-152-0036 | Henon Maps: Open Problems — Problem 36 | Show that $\mu_\phi$ satisfies the Large Deviation Principle (LDP) for H\"older continuous observables.
Namely, prove that, for any H\"older continuous observable $g$ with $\langle \mu_\phi, g\rangle=0$ and which is not a coboundary, there exists a
non-negative, strictly convex function $c$ which is defined on a neighb... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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801,085 | AMR-152-0037 | Henon Maps: Open Problems — Question 37 | Do there exist norms
for functions on the Julia set which are bounded on H\"older continuous functions, contract
(on the complement of an
invariant line) under the action of $f_*$ (or, more generally, of $f_* (e^{\phi-P(\phi)} \cdot)$),
and such that the contraction is stable by perturbation of $\phi$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 37
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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801,086 | AMR-152-0038 | Henon Maps: Open Problems — Question 38 | The case of cubic automorphisms on $\mathbb{C}^3$, and the case of automorphisms obtained as a composition of an affine transformation and a triangular one were considered by
Blanc and Van Santen [blanc-V1,blanc-V2]. Their computations lead them to formulate the following intriguing problem.
A weak Perron number is an ... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 38
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
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"display_name": "Dynamical Systems",
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,087 | AMR-152-0039 | Henon Maps: Open Problems — Question 39 | Suppose $f$ is a polynomial automorphism of $\mathbb{C}^d$ satisfying $\lambda(f)=1$.
Is it true that $\deg(f^n) \asymp n^k$ for some $k \in \mathbb{N}$? Moreover,
if $k\ge 1$, does $f$ preserve a rational fibration? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 39
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
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"display_name": "Dynamical Systems",
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"slug": "dynamical-systems",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,088 | AMR-152-0040 | Henon Maps: Open Problems — Question 40 | Urech proved that $\deg(f^n)$ tends to infinity whenever it is unbounded, see [urech].
His result was made stronger by Cantat and Xie in [CX]: there exists a universal function $\sigma\colon \mathbb{N}\to\mathbb{N}$
such that $\limsup \sigma = \infty$ and $\deg(f^n) \ge \sigma(n)$.
They raised the following weaker form... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 40
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,089 | AMR-152-0041 | Henon Maps: Open Problems — Question 41 | Let $\mathrm{Tame}(3)$ be the subgroup of polynomial automorphisms of $\mathbb{C}^3$ which is generated by affine and triangular transformations.
A theorem of Shestakov and Umirbaev [SU] states that $\mathrm{Tame}(3)$ is a strict subgroup
of the full group of polynomial automorphisms of $\mathbb{C}^3$ (as opposed to th... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 41
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,090 | AMR-152-0042 | Henon Maps: Open Problems — Question 42 | Let $f$ be any generalized H\'enon map.
Describe the set of all generalized H\'enon maps $g$ such that $\bar{S}(f)$ is biholomorphic to $\bar{S}(g)$. | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 42
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,091 | AMR-152-0043 | Henon Maps: Open Problems — Question 43 | A complex manifold which admits a holomorphic atlas whose transition maps are restriction of birational maps
of $\mathbb{P}^d_\mathbb{C}$ is said to carry a birational structure.
The following problem is extracted from [dloussky].
Does any non-K\"ahler compact complex surface admit a birational structure? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 43
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,092 | AMR-152-0044 | Henon Maps: Open Problems — Problem 44 | Let $f\in \mathrm{Aut}[\mathbb{C}^d]$ be any regular polynomial automorphism.
- Prove that one can find a compact complex manifold $\bar{S}(f)$ and an open immersion
$S(f) \subset \bar{S}(f)$ such that the complement $\bar{S}(f)\setminus S(f)$ is a divisor.
- Prove that $\bar{S}(f)$ is unique up to bimeromorphism.
-... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Problem 44
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,093 | AMR-152-0045 | Henon Maps: Open Problems — Question 45 | It is unclear how to extend this construction to a larger class of polynomial automorphisms of $\mathbb{C}^3$.
However when $\lambda(f)^2>\lambda(f^{-1})$ an invariant valuation on the ring of polynomial functions in three variables (One way to interpret geometrically such an object
is to say that it picks an irreducib... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 45
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,094 | AMR-152-0046 | Henon Maps: Open Problems — Question 46 | Over a number field $K$, is it possible to construct infinite families of generalized H\'{e}non maps of algebraic degree $d$, and $K$-rational cycles of length at least $d+3$? Can one construct maps with $N_d$ periodic points, where $N_d- d\to \infty$, or even $N_d/d\to \infty$ as $d\to\infty$? | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 46
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,095 | AMR-152-0047 | Henon Maps: Open Problems — Conjecture 47 | Let $K$ be a number field, let $B\geq 1$, and let $d\geq 2$. Then as $f$ varies over generalized H\'{e}non maps of degree $d$ over $K$, the quantity
\[\#\{P\in \operatorname{Per}(f):[K(P):K]\leq B\}\]
is bounded just in terms of $[K:\mathbb{Q}]$, $d$, and $B$. | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Conjecture 47
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
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"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,096 | AMR-152-0048 | Henon Maps: Open Problems — Conjecture 48 (see [I]) | We have already seen why this bound must depend on $d$, and adjoining periodic points of $f$ to the base field shows why the bound must depend on $[K:\mathbb{Q}]$. As a starting point for further exploration, we mention two more readily falsifiable conjectures.
Over $\mathbb{Q}$, $(x, y)\mapsto (y, y^2+c+x)$ has no po... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Conjecture 48
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: see [I] | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,097 | AMR-152-0049 | Henon Maps: Open Problems — Conjecture 49 | For all but finitely many $\delta\in \mathbb{Q}$, the $\mathbb{Q}$-rational periodic points of any $f(x, y)=(y, y^2+c-\delta x)$ with $c\in \mathbb{Q}$ have period dividing 2. | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Conjecture 49
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,098 | AMR-152-0050 | Henon Maps: Open Problems — Conjecture 50 | Let $K$ be a number field, let $B\geq 1$, and let $d\geq 2$. Then, there exist an $\epsilon>0$ and constant $C$ (depending on these data) such that, as $f$ varies over generalized H\'{e}non maps of degree $d$ over $K$, the quantity
\[\#\{P\in (\overline{K})^2 :[K(P):K]\leq B\text{ and }\hat{h}_f(P)<\epsilon h(f)+C\}\]
... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Conjecture 50
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,099 | AMR-152-0051 | Henon Maps: Open Problems — Question 51 | Under what circumstance is it true that
\[\log\operatorname{Norm}(\mathfrak{a}_n)=o(d^n) \]
as $n\to \infty$?
Under what circumstance does there exist an ideal $\mathfrak{b} \subset \mathcal{O}_{K, S}$ such
that $\mathfrak{a}_n | \mathfrak{b}$ for infinitely many $n$? Note that, since $\mathfrak{a}_1 | \mathfrak{a}_n$
... | Source list: Berger, Bedford - Henon Maps: A List of Open Problems (2023)
Source item: Question 51
Source URL: https://arxiv.org/abs/2312.03907
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Berger, Bedford | 2,023 | 11 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,100 | AMR-153-0001 | Ultraproduct II_1 Factors — Problem 1 | Classify elementary equivalence classes of $\mathbb{M}^{\mathcal{U}}$ where $\mathcal{U}$ ranges over ultrafilters on $\mathbb{N}$. What about elementary equivalence classes of $\mathbb{M}_{\mathcal{U}}$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,101 | AMR-153-0002 | Ultraproduct II_1 Factors — Problem 2 | For every Connes embeddable non Gamma II$_1$ factor $N$ does there exist an embedding $\pi: N\hookrightarrow \mathbb{M}^{\mathcal{U}}$ such that $N'\cap \mathbb{M}^{\mathcal{U}}=\mathbb{C}$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,102 | AMR-153-0003 | Ultraproduct II_1 Factors — Problem 3 | [Solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]]
A non Gamma factor $N$ is said to be pseudocompact if there exists an ultrafilter $\mathcal{U}$ such that $N$ is elementarily equivalent to $\mathbb{M}^{\mathcal{U}}$. Is $L(\mathbb{F}_n)$ pseudocompact for $n\geq 2$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,103 | AMR-153-0004 | Ultraproduct II_1 Factors — Problem 4 | Does there exist a group von Neumann algebra $L(G)$ that is pseudocompact? Does there exist an icc non inner amenable group von Neumann algebra $L(G)$ that is not pseudocompact? (Second part solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]) | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,104 | AMR-153-0005 | Ultraproduct II_1 Factors — Problem 5 | Let $N$ be a finite index subfactor of the matrix ultraproduct $\mathbb{M}^\mathcal{U}$. Then is $N$ also isomorphic to a matrix ultraproduct? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,105 | AMR-153-0006 | Ultraproduct II_1 Factors — Problem 6 | Denote by $\mathbb{S}^{\mathcal{U}}=\prod_{i\to \mathcal{U}}\mathbb{S}_n$, the ultraproduct of the symmetric groups with the normalized Hamming distance. Clearly, $\mathbb{S}^{\mathcal{U}}\subset \mathbb{M}^\mathcal{U}$ in a trace preserving way (where the trace on $\mathbb{S}^{\mathcal{U}}$ is given by one minus the u... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,106 | AMR-153-0007 | Ultraproduct II_1 Factors — Problem 7 | Recall that an embedding of $\iota: N\hookrightarrow M$ is existential if there is an embedding of $M\subset N^{\mathcal{U}}$ that restricts to the diagonal embedding under $\iota$. One can define this notion similarly for inclusions of groups.
Does there exist a separable $N$ admitting an existential embedding $L(\ma... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,107 | AMR-153-0008 | Ultraproduct II_1 Factors — Problem 8 | For some mild evidence for the above in the negative, see [jekel2024upgradedfreeindependencephenomena] wherein a general result on free complementation in $L(\mathbb{F}_2)^\mathcal{U}$ is proved, generalizing previous forms of absorption results in the literature, for instance [Popa1983, HoudayerIoana2024, CyrilAOP, Fr... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 8
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,108 | AMR-153-0009 | Ultraproduct II_1 Factors — Problem 9 | Does there exist a group $G$ that contains an existential inclusion of $\mathbb{F}_2$ such that $L(G)\ncong L(\mathbb{F}_n)$ for some $n\in \mathbb{N}$? Specifically, does there exist a non elementary surface group $G$ such that $L(G)\ncong L(\mathbb{F}_n)$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,109 | AMR-153-0010 | Ultraproduct II_1 Factors — Problem 10 | Let $M$ be a separable II$_1$ factor that contains an existential copy of $N$ where $N$ is a nonamenable biexact II$_1$ factor. Then is $M$ prime? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,110 | AMR-153-0011 | Ultraproduct II_1 Factors — Problem 11 | For the definition of bi-exactness see the work [ding2023biexactvonneumannalgebras]. The above behavior was observed in $L(\mathbb{F}_2)$, see [Sridiagonal].
Let $N$ be a non amenable II$_1$ factor with Haagerup property, and $N\subset M$ existentially. Then can $M$ have property (T)? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,111 | AMR-153-0012 | Ultraproduct II_1 Factors — Problem 12 | Let $N$ be a II$_1$ factor with Haagerup's property, and $B\subset N^\mathcal{U}$, with Property (T). Then are there finite dimensional subalgebras $M_n\subset N$ such that $B\subset \prod_{n\to \mathcal{U}}M_n$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,112 | AMR-153-0013 | Ultraproduct II_1 Factors — Problem 13 | Progress and evidence towards the above has been obtained in [peterson2026ultraproductapproximationspropertyt].
Does there exist an existential inclusion of $L(\mathbb{F}_2)$ into $\mathbb{M}^\mathcal{U}$? Is the random embedding existential, in the sense of Haar-sampling? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,113 | AMR-153-0014 | Ultraproduct II_1 Factors — Problem 14 | Recall that a II$_1$ factor $N$ is said to be existentially closed if whenever it embeds into a II$_1$ factor $M$, it can embed existentially into $M$. Such factors exist by [ECfactors], also see [IOANA2024110264, GKEPTConj] for concrete constructions.
Does there exist a countable group $G$ such that $L(G)$ is an exis... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,114 | AMR-153-0015 | Ultraproduct II_1 Factors — Problem 15 | Does there exist a sequence of separable non Gamma factors $N_i$ such that their ultraproduct $\prod_{i\to \mathcal{U}}N_i$ has Property Gamma? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 15
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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801,115 | AMR-153-0016 | Ultraproduct II_1 Factors — Problem 16 | [Solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]]
Does there exist a pair of Connes embeddable non Gamma factors that are not elementarily equivalent? Does there exist continuum many non Gamma factors that are pairwise not elementarily equivalent? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 16
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"description": "Limits, continuity, calculus, and function theory.",
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"slug": "amr-open-problem-lists",
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801,116 | AMR-153-0017 | Ultraproduct II_1 Factors — Problem 17 | [Solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]]
Does there exist an icc non inner amenable group $G$ such that $L(G)$ is not elementarily equivalent to $L(\mathbb{F}_2)$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 17
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"description": "Limits, continuity, calculus, and function theory.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,117 | AMR-153-0018 | Ultraproduct II_1 Factors — Problem 18 | [Solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]]
Are there two non elementarily equivalent Connes embeddable super McDuff II$_1$ factors $N,M$? Are there continuum many? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 18
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"description": "Limits, continuity, calculus, and function theory.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,118 | AMR-153-0019 | Ultraproduct II_1 Factors — Problem 19 | If $N$ is a super McDuff II$_1$ factor, and $N$ is elementarily equivalent to $M$ then is $M$ super McDuff? In particular, does there exist a super McDuff II$_1$ factor which is not uniformly super McDuff? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 19
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,119 | AMR-153-0020 | Ultraproduct II_1 Factors — Problem 20 | [Solved by J. Peterson [peterson2026ultraproductapproximationspropertyt]]
Does there exist two factors with property Gamma and are not McDuff, that are not elementarily equivalent? Are there continuum many such examples? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 20
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,120 | AMR-153-0021 | Ultraproduct II_1 Factors — Problem 21 | The above is complementary to [boutonnetchifanioana], which established many non elementarily equivalent McDuff factors.
Is $L(F)$ super McDuff, where $F$ is the well known Thompson's group? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 21
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,121 | AMR-153-0022 | Ultraproduct II_1 Factors — Problem 22 | See [Jolissaint1998] where it was proved that these group von Neumann algebras are McDuff.
If $M\cong N_1\overline{\otimes} N_2$, and $M$ is McDuff, does it imply that either $N_1$ or $N_2$ are McDuff? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 22
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,122 | AMR-153-0023 | Ultraproduct II_1 Factors — Problem 23 | For the next few problems, recall the equivalence relation of sequantial commutation [elayavalli2023sequential] on the haar unitaries in a II$_1$ factor. For $u,v\in \mathcal{H}(N)$ haar unitaries, say that $u\sim_{N^\mathcal{U}} v$ if there exists a finite set $w_1, \cdots, w_n$ of haar unitaries in $N^{\mathcal{U}}$,... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 23
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,123 | AMR-153-0024 | Ultraproduct II_1 Factors — Problem 24 | Does there exist a property (T) II$_1$ factor with unique sequential commutation orbit? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 24
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,124 | AMR-153-0025 | Ultraproduct II_1 Factors — Problem 25 | Does there exist a II$_1$ factor $N$ with no diffuse relative $(T)$ subalgebras and with unique sequential commutation orbit? Is there such an $N$ with additionally the Haagerup property? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 25
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
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"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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801,125 | AMR-153-0026 | Ultraproduct II_1 Factors — Problem 26 | Does there exist a II$_1$ factor $N$ satisfying $h(N)=0$ but $N$ has continuum many sequential commutation orbits? Secondly does there exist a II$_1$ factor $N$ such that $h(N)=0$, and $N$ is not generated as a von Neumann algebra by a single sequential commutation orbit? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 26
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,126 | AMR-153-0027 | Ultraproduct II_1 Factors — Problem 27 | Let $M= N_1*_B N_2$, and $u_i\in \mathcal{H}(N_i)$ such that $E_B(u_i^k)=0$ for all $k\in \mathbb{N}$. Suppose $v_i\in \mathcal{H}(M^\mathcal{U})$ such that $u_i\sim_{M^\mathcal{U}} v_i$ and $E_{B^\mathcal{U}}(v_i^k)=0$ for all $k \in \mathbb{N}$. Then is $v_1$ freely independent from $v_2$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 27
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,127 | AMR-153-0028 | Ultraproduct II_1 Factors — Problem 28 | See [HoudayerIoana2024] where this is proven for commutants.
Let $N$ be a non-prime II$_1$ factor. Does it have a unique sequential commutation orbit? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 28
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
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"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,128 | AMR-153-0029 | Ultraproduct II_1 Factors — Problem 29 | Let $N$ be a separable II$_1$ factor. Then do $N$ and $N^t$ have the same number of sequential commutation orbits? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 29
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,129 | AMR-153-0030 | Ultraproduct II_1 Factors — Problem 30 | Recall $A,B\subset M$ are $k$-independent if for all alternating centered words $w$ of length $k$ in $A,B$, one has $\tau(w)=0$. Usage of plain independent refers to $2$-independent. Additionally, $u,v\in \mathcal{U}(M)$ are $k$-independent means that the von Neumann algebras they generate are $k$-independent.
Suppose... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 30
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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801,130 | AMR-153-0031 | Ultraproduct II_1 Factors — Problem 31 (Solved by G. Patchell and A. Shiner, paper in preparation) | This is done in some particular cases in [exoticCIKE].
Suppose $u,v\in N^\mathcal{U}$ are freely independent unitaries, then can they be lifted to sequences of pairwise $k$-independent unitaries in $N$ for all $k$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 31
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Solved by G. Patchell and A. Shiner, paper in preparation | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,131 | AMR-153-0032 | Ultraproduct II_1 Factors — Problem 32 | Suppose $M$ is a separable subfactor admitting two embeddings $\pi_i:M\to N^\mathcal{U}$ and further suppose $\varphi_n:N\to N$ are a sequence of unital completely positive maps, such that $\Phi= (\varphi_n)_{\mathcal{U}}$ conjugates $\pi_1$ to $\pi_2$. Then does there exist a unitary $u\in N^\mathcal{U}$ that conjugat... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 32
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,132 | AMR-153-0033 | Ultraproduct II_1 Factors — Problem 33 | Is there a non amenable separable II$_1$ factor $N$ such that any pair of embeddings of $N$ into $N^{\mathcal{U}}$ are conjugate by a unitary in $N^{\mathcal{U}}$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 33
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,133 | AMR-153-0034 | Ultraproduct II_1 Factors — Problem 34 | If a Connes embeddable separable II$_1$ factor $N$ satisfies that any pair of embeddings of $N$ into $R^{\mathcal{U}}$ are conjugate by an automorphism of $R^{\mathcal{U}}$, then is $N\cong R$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 34
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,134 | AMR-153-0035 | Ultraproduct II_1 Factors — Problem 35 | See [ScottSri2019ultraproduct, AGKE] for a detailed discussion of such Jung-type properties ([JungTubularity]) and what is known and not known.
Is the pentagon right angled Artin group II$_1$-factor stable? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 35
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,135 | AMR-153-0036 | Ultraproduct II_1 Factors — Problem 36 (II$_1$ factor Tarski's problem) | Are the factors $L(\mathbb{F}_n)$ elementarily equivalent for different values of $n$? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 36
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: II$_1$ factor Tarski's problem | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,136 | AMR-153-0037 | Ultraproduct II_1 Factors — Problem 37 | The reduced $C^*$-algebra version of this problem has been settled in the negative in the recent work [elayavalli2025negativeresolutioncalgebraictarski].
The problem below is due to S. Popa:
Let $N$ be a Connes embeddable separable II$_1$ factor. Does it admit an embedding into $R^\mathcal{U}$ with factorial commutan... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 37
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,137 | AMR-153-0038 | Ultraproduct II_1 Factors — Problem 38 | Let $N_0$ be an index $2$ subfactor of an ultrapower $N^\mathcal{U}$. Then is $N_0\cong \prod_{i\to \mathcal{U}} N_i$ where $N_i\subset N$ are index $2$ subfactors? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 38
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,138 | AMR-153-0039 | Ultraproduct II_1 Factors — Problem 39 | Is $N^{\mathcal{U}}$ ever isomorphic to a group von Neumann algebra? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 39
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,139 | AMR-153-0040 | Ultraproduct II_1 Factors — Problem 40 | It follows from arguments of S. Popa [PopaOrthoPairs] that ultrapowers can never be non trivial tensor products, crossed products, amalgamated free products, or have diffuse regular abelian subalgebras.
Does there exist a II$_1$ factor $N$ such that $h(N^{\mathcal{U}})=\infty$ and $h(N)=0$, where $h$ denotes 1-bounded... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 40
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,140 | AMR-153-0041 | Ultraproduct II_1 Factors — Problem 42 | The above ``*ultrapower-bicommutant* problem'' is credited to S. Popa, see [Popaindep].
If $M$ is a II$_1$ factor, then does $\mathbb{M}_2(\mathbb{C}) \otimes M$ always embed into $M^\mathcal{U}$? (Note this is immediate if $M$ is Connes embeddable.) | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 42
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,141 | AMR-153-0042 | Ultraproduct II_1 Factors — Problem 43 | Recall that a II$_1$ factor $N$ is said to be solid if any subalgebra $A\subset N$ with diffuse commutant in $N$ is amenable. Recall that a II$_1$ factor $N$ is said to be $\mathcal{U}$-solid if any subalgebra $A\subset N$ with diffuse commutant in $N^\mathcal{U}$ is amenable.
Is solidity equivalent to $\mathcal{U}$-s... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 43
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,142 | AMR-153-0043 | Ultraproduct II_1 Factors — Problem 44 | See Proposition 7 in [OzawaSolidActa] (see also [HURigid]). The problem is still open.
Is there a pair of II$_1$ factors with the same 2-quantifier theory but are not elementarily equivalent? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 44
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,143 | AMR-153-0044 | Ultraproduct II_1 Factors — Problem 45 | For the definition of 2-quantifier theory, please consult [quantifiertheory].
Does there exist II$_1$ factors $N,M$ that are elementarily equivalent, but not as as $C^*$-algebras? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 45
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,144 | AMR-153-0045 | Ultraproduct II_1 Factors — Problem 46 | Is every seperable II$_1$ factor selfless as a $C^*$-algebra? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 46
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
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"display_name": "Analysis",
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"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 13,
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"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,145 | AMR-153-0046 | Ultraproduct II_1 Factors — Problem 47 | For a definition of selfless see [robertselfless]. This is known for all ultraproduct II$_1$ factors, and some select other examples. Also recall that it is known that strict comparison holds for all II$_1$ factors viewed as $C^*$-algebras.
Does there exist a II$_1$ factor $N$ such that $N^\mathcal{U}$ has non-full fu... | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 47
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,146 | AMR-153-0047 | Ultraproduct II_1 Factors — Problem 48 | Suppose $N_1, N_2, M_1, M_2$ are separable II$_1$ factors such that $N_1^\mathcal{U}\overline{\otimes} N_2^\mathcal{U}\cong M_1^\mathcal{U}\overline{\otimes} M_2^\mathcal{U}$, then is $N_i$ elementarily equivalent to $M_i$ up to permutation? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 48
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,147 | AMR-153-0048 | Ultraproduct II_1 Factors — Problem 49 | Suppose $I,J$ are finite sets, and $\{N_i\}_{i\in I}, \{M_j\}_{j\in J}$ are separable II$_1$ factors such that $*_{i\in I}N_i^\mathcal{U}\cong *_{j\in J}M_j^\mathcal{U}$, then is $I\cong J$ and the factors are mutually elementarily equivalent up to permutation? | Source list: Elayavalli - 50 Open Problems: Ultraproduct II_1 Factors (2025)
Source item: Problem 49
Source URL: https://arxiv.org/abs/2511.20377
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Elayavalli | 2,025 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,148 | AMR-154-0001 | Nijenhuis Geometry and Integrable Systems — Problem 1 | For the KdV system, this was reported to be done already in [veselov], though we did not find detailed formulas. The booklet [moser81] relates stationary solutions of the KdV to the solutions of the Neumann systems. Namely, it is shown that the potential energy of the Neumann system evaluated along the trajectory and s... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,149 | AMR-154-0002 | Nijenhuis Geometry and Integrable Systems — Problem 2 | \begin{Problem} Can one write the system of equations in such a way that its coefficients depend on $L$ only (at least in the $\mathrm{gl}$-regular case)? \end{Problem}
Note that in the $\mathrm{gl}$-regular case any two pairs $(L_1,e_1)$ and $(L_2, e_2)$ with identical Jordan blocks of $L_1$ and $L_2$ are isomorphic b... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 2
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,150 | AMR-154-0003 | Nijenhuis Geometry and Integrable Systems — Problem 3 | Why is the WDVV equation interesting? What are its applications? Is it possible to reformulate the part which is interesting for application by replacing the solution of these equations with a pair $(L,e)$, at least in the $\mathrm{gl}$-regular case? What pairs $(L,e)$ appear in known examples of Frobenius manifolds? | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,151 | AMR-154-0004 | Nijenhuis Geometry and Integrable Systems — Problem 4 | Given a Nijenhuis operator $L$, describe all of its (local) conservation laws (of course, the same question can be asked for any operator, not necessarily Nijenhuis, see below discussion on superintegrable potentials). | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,152 | AMR-154-0005 | Nijenhuis Geometry and Integrable Systems — Problem 5 | Which Nijenhuis operators admit (The answer is known near almost every points and follows from the local description of geodesically compatible pairs in [splitting2, splitting1]. The question is most interesting near singular points of the Nijenhuis operator.) at least one geodesically compatible metric $g$?
Given $L$,... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,153 | AMR-154-0006 | Nijenhuis Geometry and Integrable Systems — Problem 6 | We have a complete classification of $\mathrm{gl}$-regular Nijenhuis operators in dimension 2 as a list of explicit normal forms. Describe all conservation laws for each of these operators. Or at least, find one regular conservation law for each of them. | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,154 | AMR-154-0007 | Nijenhuis Geometry and Integrable Systems — Problem 7 | Next, if we have a regular conservation law $f$ for $L$, then we should be able to construct a companion coordinate system and then
get a metric $g$ geodesically compatible with $L$, by using the above mentioned explicit formula from [nijappl5].
For each $\mathrm{gl}$-regular Nijenhuis operator $L$ in dimension 2, con... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,155 | AMR-154-0008 | Nijenhuis Geometry and Integrable Systems — Problem 8 | \begin{Problem}
For each $\mathrm{gl}$-regular Nijenhuis operator $L$ in dimension 2, construct (explicitly) a geodesically compatible metric. \end{Problem}
Generalise the above mentioned formula from [nijappl5] to an arbitrary coordinate system $x^1,\dots, x^n$ assuming that in this coordinate system we have a conser... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 8
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,156 | AMR-154-0009 | Nijenhuis Geometry and Integrable Systems — Problem 9 | \begin{Problem} Generalise the above mentioned formula from [nijappl5] to an arbitrary coordinate system $x^1,\dots, x^n$ assuming that in this coordinate system we have a conservation law given as an explicit function $f(x^1,\dots, x^n)$. \end{Problem}
Construct new explicit examples of metrics geodesically compatibl... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,157 | AMR-154-0010 | Nijenhuis Geometry and Integrable Systems — Problem 10 | Are geometric Poisson structures of any order greater than 1 projectively invariant? Can one interpret the leading coefficient $g^{ij}$ as a projectively invariant object? | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,158 | AMR-154-0011 | Nijenhuis Geometry and Integrable Systems — Problem 11 | Certain Frobenius manifolds seem to give examples of geometric Poisson bracket of order 3
(at least, the WDVV equation does it). Is Frobenius structure projectively invariant? Can one replace, in the definition of Frobenius structure, the flat metric by a metric of constant curvature? | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,159 | AMR-154-0012 | Nijenhuis Geometry and Integrable Systems — Problem 12 | \begin{Problem}
Certain Frobenius manifolds seem to give examples of geometric Poisson bracket of order 3
(at least, the WDVV equation does it). Is Frobenius structure projectively invariant? Can one replace, in the definition of Frobenius structure, the flat metric by a metric of constant curvature?
\end{Problem}
As ... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,160 | AMR-154-0013 | Nijenhuis Geometry and Integrable Systems — Problem 13 | \begin{Problem}
As we mentioned above, geometric Poisson brackets of order 3 are essentially the same as Killing tensors whose covariant derivative satisfies a certain relation, and certain Forbenius manifolds were used to construct such Killing tensors. Does there exists a construction of a Killing tensor by a Frobeni... | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,161 | AMR-154-0014 | Nijenhuis Geometry and Integrable Systems — Problem 14 | Describe all geometric Poisson structures of the first order compatible with a geometric Poisson structure of the third order which is not Darboux-Poisson. How big can the compatible pencil of such first order structures be? | Source list: Bolsinov, Konyaev, Matveev - Research Problems on Nijenhuis Geometry and Integrable Systems (2024)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2410.04276
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bolsinov, Konyaev, Matveev | 2,024 | 6 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,162 | AMR-155-0001 | Open Problems in Wavelet Theory — Problem 1 | One of the fundamental areas in the theory of wavelets is the investigation of properties of the collection of all wavelets as a subset of $L^2(\mathbb{R})$. The most prominent problem in this area was formulated independently by D. Larson and G. Weiss around the year 1995.
Is the collection of all orthonormal wavelet... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,163 | AMR-155-0002 | Open Problems in Wavelet Theory — Conjecture 2 | Let $\mathscr D$ be any wavelet dimension function, i.e., $\mathscr D$ satisfies (D1)--(D4). Then, the collection of o.n. wavelets with the same dimension function
\[
\{\psi \in L^2(\mathbb{R}): \psi \text{ is an o.n. wavelet and } \mathscr D_\psi=\mathscr D\}.
\]
is a path connected subset of $L^2(\mathbb{R})$. | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,164 | AMR-155-0003 | Open Problems in Wavelet Theory — Problem 3 | This leaves open the problem of existence of Riesz wavelets which was posed by Seip [Seip]. We say that $\psi$ is a Riesz wavelet for $\mathcal{H} =H^2(\mathbb{R})$ or $L^2(\mathbb{R})$ if the wavelet system is a Riesz basis of $\mathcal{H}$. A Riesz basis in a Hilbert space $\mathcal{H}$ can be defined as an image of ... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,165 | AMR-155-0004 | Open Problems in Wavelet Theory — Problem 4 | Larson [La2] has posed an interesting problem about frequency supports of wavelets. Must the support of the Fourier transform of a wavelet contain a wavelet set? This problem stems from the observation that there are two ways of describing minimality of frequency support. The first one is that $\operatorname{supp} \hat... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,166 | AMR-155-0005 | Open Problems in Wavelet Theory — Problem 5 | Another fundamental problem posed by Larson [La2] asks about density of Riesz wavelets.
Is the collection of all Riesz wavelets dense in $L^2(\mathbb{R})$? | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,167 | AMR-155-0006 | Open Problems in Wavelet Theory — Problem 6 | Suppose that $\psi \in L^2(\mathbb{R}^n)$ is a Parseval wavelet. Then, we can define spaces
\[
V_j = D^j(V(\psi)) \qquad j\in {\mathbb{Z}},
\]
where $Df(x)=\sqrt{2} f(x)$ is a dilation operator. Baggett has shown that a sequence $\{V_j:j\in{\mathbb{Z}}\}$ satisfies all properties of GMRA (M1), (M2), (M4), and (M5') pos... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,168 | AMR-155-0007 | Open Problems in Wavelet Theory — Problem 7 | A more recent problem was proposed by Christensen and his collaborators [CKK1, CKK2].
Suppose $\psi$ is Bessel wavelet with bound $<1$. Does there exist $\psi'$ such that the combined wavelet system
\[
\{\psi_{j,k}: j,k \in {\mathbb{Z}}\} \cup \{\psi'_{j,k}: j,k \in {\mathbb{Z}}\}.
\]
generated by $\psi$ and $\psi'$ i... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
801,169 | AMR-155-0008 | Open Problems in Wavelet Theory — Problem 8 | The last problem illustrates the difficulty of determining whether a function is a frame wavelet or not. The following problem was proposed by Weber and the first author [BW].
For $0<b<1$ define $\psi_b \in L^2(\mathbb{R})$ by $\hat \psi_b =
\mathbf 1_{(-1,-b) \cup (b, 1)}$.
For what values of $1/8< b \le 1/6$, is $\p... | Source list: Bownik, Rzeszotnik - Open Problems in Wavelet Theory (2019)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1905.08230
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bownik, Rzeszotnik | 2,019 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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