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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,070 | AMR-115-0011 | Foliations and Diffeomorphism Groups — Question 11 | Nicola Pia has some work constraining the dynamics of the kernel line field $\mathcal{W}$, but overall we know very little. A crucial remark is that there is no stability for Engel structures, meaning that perturbing an Engel structure will produce some other Engel structure that in general won't be diffeomorphic to th... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 11
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,071 | AMR-115-0012 | Foliations and Diffeomorphism Groups — Question 12 | How does one systematically produce examples of a contact 3-manifold $(M,\xi)$, a line field $L$ tangent to $\xi$, and a non-vanishing closed 2-form $\omega$, of integral class, annihilating $L$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 12
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,072 | AMR-115-0013 | Foliations and Diffeomorphism Groups — Question 13 | Another topic that is of interest is whether Engel structures interact with other geometric structures. Here are two questions:
Consider a $4$-manifold endowed with a foliation $\mathcal{F}$ by surfaces. Can the foliation be perturbed to an Engel structure? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 13
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,073 | AMR-115-0014 | Foliations and Diffeomorphism Groups — Question 14 | Consider a $4$-manifold endowed with a codimension-$1$ foliation $\mathcal{F}$. Suppose moreover that there is a plane field $\xi \subset T\mathcal{F}$ that is a leafwise contact structure. Assume that $\xi$ splits as a sum of line fields. Can this data be perturbed to an Engel structure? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 14
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,074 | AMR-115-0015 | Foliations and Diffeomorphism Groups — Question 15 | I would like to conquer some doubt on Palmeira's theorem for foliation by planes $\mathcal{F}$ of $\mathbb{R}^3$.
In his paper there is a proposition saying that an infinite braid can be extended as an isotopy of plane, which has counter-examples. This is used to show that the leaf space determines the foliation.
Find... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 15
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,075 | AMR-115-0016 | Foliations and Diffeomorphism Groups — Question 16 | Let $\omega$ be a volume-form on $**S**^2$ and $\mathrm{Diff}_0(**S**^2, \mathrm{vol})$ be the group of volume-preserving diffeomorphisms of the 2-sphere that are in the same component as the identity map. The isomorphism type of the group $\mathrm{Diff}_0(**S**^2, \mathrm{vol})$ does not depend on the choice of $\omeg... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 16
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,076 | AMR-115-0017 | Foliations and Diffeomorphism Groups — Question 17 | Let $\text{Diff}_0(**D**^2, *)$ be the group of smooth orientation-preserving diffeomorphisms of $**D**^2$ that fix a marked point $*$ say at the origin. There are two bounded Euler classes on this group; one is induced by the restriction to the boundary and the other is by taking derivative at the origin. The differen... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 17
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,077 | AMR-115-0018 | Foliations and Diffeomorphism Groups — Question 18 | Using the Bott vanishing theorem, Morita showed that the MMM classes $\kappa_i$ for surface bundles vanish in $H^*(\mathrm{Diff}(\Sigma_g);\mathbb{R})$ for $i>2$. Do they also vanish in bounded cohomology $H^*_b(\mathrm{Diff}(\Sigma_g); \mathbb{R})$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 18
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,078 | AMR-115-0019 | Foliations and Diffeomorphism Groups — Question 19 | By now, there are several constructions of simple orderable groups [hyde2019finitely,hyde2023finitely, hyde2023two,bon2020groups]. However, only the examples in [hyde2023finitely] of Hyde and Lodha are finitely presented. In fact, they are even of type $F_\infty$. Recall a group $G$ is of type $F_n$ if there is a $K(G,... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 19
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,079 | AMR-115-0020 | Foliations and Diffeomorphism Groups — Question 20 | If one drops the orderable condition, there are two constructions [skipper2019simple, belk2022twisted]. A related question of Navas [navas2018group, Question 8] was the following: does there exist a finitely generated, left-orderable group $G$ without surjection onto $\mathbb{Z}$ and $H^2_b(G, \mathbb{R}) = 0$? The que... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 20
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,080 | AMR-115-0021 | Foliations and Diffeomorphism Groups — Question 21 (Well-Known) | Another interesting question would be to find simple orderable groups of finite cohomological dimension. A candidate would be the Burger-Mozes groups [burger2000lattices].
Are Burger--Mozes' examples of simple groups orderable? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 21
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Well-Known | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,081 | AMR-115-0022 | Foliations and Diffeomorphism Groups — Question 22 (Freedman) | Is that true that for small $\epsilon>0$, we have $g_{\mathscr{E}(p)}(\epsilon) \geq \frac{c|\mathscr{E}(p)|}{\epsilon^2+O(\epsilon^3)}$, for some constant $c$ (perhaps $c=2\pi$)? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 22
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Freedman | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,082 | AMR-115-0023 | Foliations and Diffeomorphism Groups — Question 23 | Suppose $\epsilon>0$ is a small number. We have a representation $\rho\colon \pi_1(\Sigma_g) \to \mathrm{Diff}_0(**S**^1)$ such that for a generating set $S$ of $\pi_1(\Sigma_g)$, the set $\rho(S)$ are diffeomorphisms that are at most $\epsilon$ away from $\mathrm{PSL}_2(\mathbb{R})$. Can we bound the GV class for the ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 23
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,083 | AMR-115-0024 | Foliations and Diffeomorphism Groups — Question 24 | Is there a geometric proof of the above theorem? i.e. can one find a family of representations of a fundamental group of $4$-manifolds into $\mathrm{Homeo}_0(**S**^3)$ that exhibits the unboundedness of the Euler class? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 24
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,084 | AMR-115-0025 | Foliations and Diffeomorphism Groups — Question 25 (Freedman) | Suppose $**S**^3\to **S**^7\to **S**^4$ is a ``generalized'' Hopf fibration. Does there exist a homology $4$-sphere $H$ and a degree one map $H\to **S**^4$ such that the pull-back of the generalized Hopf fibration is a flat $**S**^3$-bundle? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 25
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Freedman | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,085 | AMR-115-0026 | Foliations and Diffeomorphism Groups — Question 26 | Suppose we are given an $**S**^3$-bundle $**S**^3\to E\xrightarrow{p} M$ over a $4$-manifold $M$ with nontrivial Euler class and $p_1$. Mather-Thurston's theory says we can find a bordism of this bundle to a $C^0$-flat bundle $**S**^3\to E'\to M'$. Can one bound the simplicial volume of $M'$ so that it does not depend ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 26
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,086 | AMR-115-0027 | Foliations and Diffeomorphism Groups — Question 27 | Let $M$ be a closed hyperbolic 3-manifold whose first Betti number is at least one. Is every integral second cohomology class $a \in H^2(M ; \mathbb{R})$ of dual Thurston norm one realised as the Euler class of some representation $\rho \colon \pi_1(M) \rightarrow \mathrm{Homeo}_+(**S**^1)$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 27
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,087 | AMR-115-0028 | Foliations and Diffeomorphism Groups — Question 28 | Hirsch and Thurston [hirsch1975foliated] proved that the Euler class of amenable actions on spheres $**S**^{2n-1}$ should vanish. This is interesting because now using bounded cohomology techniques, we know a non-constructive proof that the Euler class for flat $**S**^{2n-1}$ bundles when $n>1$ is unbounded. However, b... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 28
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,088 | AMR-115-0029 | Foliations and Diffeomorphism Groups — Question 29 | In a recent work with Fournier and Monod [fournier2024bounded], we showed that in fact $\text{Homeo}_0(\mathbb{R}^n)$ is bounded acyclic for all $n$. Therefore, in particular, the Euler class for actions on $\mathbb{R}^{2n}$ is unbounded. But we do not know if the analog of Hirsch--Thurston still holds in these cases.
... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 29
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,089 | AMR-115-0030 | Foliations and Diffeomorphism Groups — Question 30 (Calegari) | Calegari's paper has many interesting points about the Euler class and planar group actions, but here I want to emphasize one of his questions:
Do analytic actions of surface groups on $\mathbb{R}^2$ satisfy the Milnor--Wood inequality? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 30
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Calegari | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,090 | AMR-115-0031 | Foliations and Diffeomorphism Groups — Question 31 | Do volume preserving actions of surface groups on $\mathbb{R}^2$ satisfy the Milnor--Wood inequality? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 31
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,091 | AMR-115-0032 | Foliations and Diffeomorphism Groups — Question 32 | Under what condition on the holonomy of a compact leaf $L$ in a $C^0$ transversally oriented foliation of codimension $>1$, the leaf $L$ is stable? For example, suppose $\mathcal{F}$ is a $C^0$ codimension $2$ foliation and $L$ is a compact leaf whose normal microbundle has a trivial Euler class, its fundamental group ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 32
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,092 | AMR-115-0033 | Foliations and Diffeomorphism Groups — Question 33 | Consider a foliation $\mathcal{F}$ defined by a fibration with closed basis $B$ and fiber $F$ and $\pi_1(F)=\mathbb{Z}^k$. Under what hypothesis does any foliation $\mathcal{G}$ close to $\mathcal{F}$ have a compact leaf close to a fiber? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 33
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,093 | AMR-115-0034 | Foliations and Diffeomorphism Groups — Question 34 | Let $\mathcal{F}$ be the foliation defined by a fibration $\pi\colon M\to S$ where $S$ is a genus $2$ closed oriented surfaces and the fiber is the torus $T^2$. Under what hypothesis on the monodromy does any foliation $\mathcal{G}$ close to $\mathcal{F}$ have a compact leaf close to a fiber? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 34
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,094 | AMR-115-0035 | Foliations and Diffeomorphism Groups — Question 35 | One says that two commuting vector fields $(U,V)$ on $\tilde S$ are $\rho$-equivariant if
for any $p$ and $\gamma\in\pi_1(S)$ one has
\[ (U(\varphi(\gamma) (p)) , V(\varphi(\gamma)(p))= \rho(\gamma)(U(p),V(p)), \]
where $A(U,V) =(aU+bV, cU+dV))$ if $A$ is the matrix
$$\left(
\begin{array}{cc}
a & b\\
c & d
\end{array}
... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 35
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,095 | AMR-115-0036 | Foliations and Diffeomorphism Groups — Question 36 | Elon Lima proved that commuting vector fields for the trivial representation have a common zero.
I build an example of $C^1$ commuting pair of vector fields with no common zero, equivariant by $\rho$ if $\rho(\pi_1(S))$ is generated by a unique hyperbolic matrix.
This question is essentially equivalent to the followin... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 36
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,096 | AMR-115-0037 | Foliations and Diffeomorphism Groups — Question 37 | Prove every leaf of a $C^r$-generic codimension $1$ oriented and co-oriented foliation on a $3$-manifold has genus $<2$. | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 37
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,097 | AMR-115-0038 | Foliations and Diffeomorphism Groups — Question 38 | Consider four local $C^r$ diffeomorphisms $f_a,f_b,f_c,f_d$ of $R$ whose definition domain contains $[-1,1]$ and having $0$ as a common fixed point. Let $h=[f_a,f_b][f_c,f_d]$ be the product of the commutators.
Does there exist $\tilde f_a,\tilde f_b, \tilde f_c,\tilde f_d$ coinciding with $f_a,f_b,f_c,f_d$ out of $[-... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 38
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,098 | AMR-115-0039 | Foliations and Diffeomorphism Groups — Question 39 | Let $\mathrm{Hom}_k(\mathbb{Z}^2, \mathrm{Homeo}_0(\mathbb{R}^2))$ be the subspace of $\mathbb{Z}^2$-actions on $\mathbb{R}^2$ whose Euler number is $k$. Are subspaces $\mathrm{Hom}_k(\mathbb{Z}^2, \mathrm{Homeo}_0(\mathbb{R}^2))$ connected for each integer $k$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 39
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,099 | AMR-115-0040 | Foliations and Diffeomorphism Groups — Question 40 | Since our knowledge of the commuting diffeomorphisms of the circle has deepened by the works of Navas, Eynard-Bontemps and others, I would like to pose the following question again 40 years after my paper.
For commuting diffeomorphisms $f$ and $g$ of $**S**^1$, to what extent we can say that
the 2 cycle $(f,g)-(g,f)$ ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 40
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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800,100 | AMR-115-0041 | Foliations and Diffeomorphism Groups — Question 41 | For which $f\in\operatorname{Diff}^1(M)$, does one have \[\operatorname{CritCent}(f)>\operatorname{CritReg}(f)?\]
What are the possible values of $\operatorname{CritCent}(f)$ in this case? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 41
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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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 |
800,101 | AMR-115-0042 | Foliations and Diffeomorphism Groups — Question 42 | Consider a group action $\Phi: G\to \text{Homeo}^+(\mathbb{R}^2)$ on the plane preserving 2 transverse (maybe with prong singularities) foliations $\mathcal{F}^+$ and $\mathcal{F}^-$.
This action always extends [bonatti2024action] to *the circle at infinity* associated to the pair of foliations $(\mathcal{F}^+,\mathcal... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 42
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,102 | AMR-115-0043 | Foliations and Diffeomorphism Groups — Question 43 | Is there an action $\varphi$ on $**S**^1$ which is induced by a topological action $\Phi$, but is not induced by any smooth action $\Psi$ on $\mathbb{R}^2$ preserving two transverse foliations? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 43
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
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"name": "L3: Advanced",
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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 |
800,103 | AMR-115-0044 | Foliations and Diffeomorphism Groups — Question 44 | Which pairs $\Lambda, \Lambda'$ of (possibly non-Hausdorff) simply connected 1-manifolds can be realized as the leaf spaces of a pair of transverse foliations of the plane? What if you replace "pair" by ``triple"?
One can also specialize this to the pairs of stable/unstable leaf spaces for Anosov flows, it is as yet n... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 44
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,104 | AMR-115-0045 | Foliations and Diffeomorphism Groups — Question 45 | Let $G$ be a finitely generated amenable orderable group, and $\varphi\colon G\to \mathrm{Homeo}_+\mathbb{R}$ an action of $G$ without global fixed points. Is it true that $\varphi$ is either semi-conjugate to an affine action or laminar? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 45
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,105 | AMR-115-0046 | Foliations and Diffeomorphism Groups — Question 46 | Which pair of prelaminations forces any group action that preserves it to induce an Ansov-like action on the corresponding bifoliated plane? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 46
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,106 | AMR-115-0047 | Foliations and Diffeomorphism Groups — Question 47 | Related to the Anosov-like action conjecture, Baik-Wu-Zhao [baik2024reconstruction] recently defined a flowable group action on the bifoliated plane, and showed that if a group admits a flowable orientation-preserving action on a bifoliated plane, the group is the fundamental group of a 3-manifold with a pseudo-Anosov ... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 47
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"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"
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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 |
800,107 | AMR-115-0048 | Foliations and Diffeomorphism Groups — Question 48 | The known examples of groups with a veering pair of invariant laminations are the fundamental groups of 3-manifolds with either a pseudo-Anosov flow without perfect fits or a veering triangulation. The following is a natural question from this.
Classify all 3-manifolds whose fundamental group admits an action on $**S*... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 48
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,108 | AMR-115-0049 | Foliations and Diffeomorphism Groups — Question 49 (Calegari) | Calegari once conjectured that laminar groups preserving a very full lamination (a lamination all of whose gaps are finite-sided ideal polygons) should be residually finite. The moral of this conjecture is that preserving a lamination with enough structure should restrict the possible algebraic structure of the group.
... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 49
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Calegari | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
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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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"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 |
800,109 | AMR-115-0050 | Foliations and Diffeomorphism Groups — Question 50 | A theorem of Michel Herman says that in the group of $\mathrm{Diff}_+^\infty(**S**^1)$, every element with diophantine rotation number is $C^\infty$ conjugate to a rotation. Using that the rotation number is a continuous function, it follows easily that every element is the product of a rotation and of a conjugate to a... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 50
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,110 | AMR-115-0051 | Foliations and Diffeomorphism Groups — Question 51 | We can ask the same question, say, in $\mathrm{Diff}_0^\infty(**S**^2)$.
Here is a variation on $\mathrm{Diff}_0^\infty(\Sigma_g)$, where $\Sigma_g$ is surface of genus $g \geq 1$. After the work of Bowden, Hensel and Webb using their fine curve graph [bowden2022quasi], we know that the stable commutator length is unbo... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 51
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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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"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 |
800,111 | AMR-115-0052 | Foliations and Diffeomorphism Groups — Question 52 | Likewise, on these groups we may define the *flow length* as the word length for the set $\mathcal{S}$ of all time one map of flows, which generates $\mathrm{Homeo}_0(M)$ or $\mathrm{Diff}_0^\infty(M)$ since these groups are simple.
This norm (or its asymptotic version) measures in some sense the dynamical complexity o... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 52
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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,
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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 |
800,112 | AMR-115-0053 | Foliations and Diffeomorphism Groups — Question 53 | Let $G$ denote the group of area and orientation preserving homeomorphisms of the 2-sphere, and $[G,G]$ its subgroup generated by commutators. We recently proved ([cristofaro2023pfh], see also [cristofaro2024proof, cristifaro-gardiner2022quantitative]) that $G$ is not perfect, i.e.
\[ [G,G]\varsubsetneq G\]
However, th... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 53
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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,
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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 |
800,113 | AMR-115-0054 | Foliations and Diffeomorphism Groups — Question 54 | We will call an element that satisfies the conclusion of the proposition non-spreading.
Is the converse true? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 54
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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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"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 |
800,114 | AMR-115-0055 | Foliations and Diffeomorphism Groups — Question 55 | Is it true that a non-spreading homeomorphism of the $2$-torus has conjugates arbitrarily close to a rotation ? \\
Is it true that a non-spreading homeomorphism of a higher genus surface has conjugates arbitrarily close to the identity? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 55
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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"
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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 |
800,115 | AMR-115-0056 | Foliations and Diffeomorphism Groups — Question 56 | Let's consider the group $\mathcal{G}^r$ of germs of $C^r$ diffeomorphisms about the origin in $\mathbb{R}$, where $r$ is at least $1$ (the reason for excluding $r=0$ is that, in the continuous setting, every 1-dimensional germ -or homeomorphism- is a distortion element, because every nontrivial element is conjugate to... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 56
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,116 | AMR-115-0057 | Foliations and Diffeomorphism Groups — Question 57 | For the case of real-analytic codimension 1 foliations, the presence of an exceptional minimal set implies that an extremal leaf (passing through an endpoint of an interval of its complement in a transversal section) has infinitely many ends.
Can the above theory for the analytic group actions be generalized to the ca... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 57
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,117 | AMR-115-0058 | Foliations and Diffeomorphism Groups — Question 58 | Classify the exceptional minimal sets for codimension-$q$ foliations of compact manifolds, for $q \geq 2$ and $r \geq 2$. | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 58
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,118 | AMR-115-0059 | Foliations and Diffeomorphism Groups — Question 59 | Give an example of $\chi^2\ne 0$, namely,
construct a flat $**S**^1$-bundle over some oriented closed 4-manifold $M$
with $\chi^2\ne 0 \in H^4(M;{\mathbb{Z}})$. | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 59
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,119 | AMR-115-0060 | Foliations and Diffeomorphism Groups — Question 60 | Nothing is known about the power of the Euler class
for real analytic flat $**S**^1$-bundles.
$\chi_{\mathbb{Q}}^k\ne 0 \in
H^{2k}(B\mathrm{Diff}_+^\omega(**S**^1)^{\delta}; {\mathbb{Q}})$ for $k\geq 2$ ? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 60
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,120 | AMR-115-0061 | Foliations and Diffeomorphism Groups — Question 61 | Consider the subgroup $R_1$ of $G_1$ which consists of rotations. For $n\in \mathbb{N}$, we put
$R_n=p_n^{-1}(R_1)$. Then as a topological group, $R_1$ is isomorphic to $\mathbb{R}/\mathbb{Z}$;
\[
R_1\cong R_1\cong\cdots \cong R_ n \cdots\cong \mathbb{R}/\mathbb{Z}
\]
We fix these isomorphisms. For $n\in \mathbb{N}$, l... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 61
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,121 | AMR-115-0062 | Foliations and Diffeomorphism Groups — Question 62 | Is the subgroup $\langle \mathrm{PSL}(2)^{(k)},\mathrm{PSL}(2)^{(l)}\rangle$ in $\mathrm{Diff}^{\omega}(**S**^1)$ isomorphic to the amalgamated product $\mathrm{PSL}(2)^{(k)}*_{\mathrm{SO}(2)}\mathrm{PSL}(2)^{(l)}$? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 62
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,122 | AMR-115-0063 | Foliations and Diffeomorphism Groups — Question 63 (``Haefliger-Thurston conjecture") | The following questions, which
seem to resist to the contemporary attempts,
all ask for some triviality in the homotopy of
$B\Gamma$, that would imply the existence of foliations,
as well as some acyclicity in the homology
of some diffeomorphism groups.
On the other hand, if the
answers were negative,
it would mean tha... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 63
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: ``Haefliger-Thurston conjecture" | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,123 | AMR-115-0064 | Foliations and Diffeomorphism Groups — Question 64 (Hurder-Vogt [hurder1993product,hurder2005problem,langevin1992list]) | Consider the $\bar\Gamma_q$-structure $\gamma$ on the manifold $SO(q)$
whose microfoliation is the suspension of the canonical
action of $SO(q)$ on $\mathbb{R}^q$. Is $\gamma$
null-homotopic in $B\bar\Gamma_q$ ? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 64
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Hurder-Vogt [hurder1993product,hurder2005problem,langevin1992list] | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,124 | AMR-115-0065 | Foliations and Diffeomorphism Groups — Question 65 (``Foliations with only one leaf": see Tsuboi [tsuboi1984gamma1]) | \
Let $\Gamma_q$ be the groupoid of the germs of
local
diffeomorphisms of $\mathbb{R}^q$, and $G_q\subset\Gamma_q$
be the subgroup fixing $0$. Let $B\bar G_q$ be the
homotopy-theoretic fibre of the map
$BG_q\to BGL_q(\mathbb{R})$ classifying the normal bundle
of the universal $G_q$-structure.
Is $B\bar G_q$
homotopical... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 65
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: ``Foliations with only one leaf": see Tsuboi [tsuboi1984gamma1] | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,125 | AMR-115-0066 | Foliations and Diffeomorphism Groups — Question 66 (E. Ghys, appendix to
[molino1988riemannian]) | This amounts to asking if
any (framed)
Haefliger structure whose microfoliation has
the zero section as a leaf is homotopically trivial.
Tsuboi answered positively for $q=1$.
\
i) Is every codimension-$q$ Riemannian
foliation homotopically trivial in $B\Gamma_q$ ?
ii) Is every codimension-$q$ Lie
foliation homotopic... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 66
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: E. Ghys, appendix to
[molino1988riemannian] | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,126 | AMR-115-0067 | Foliations and Diffeomorphism Groups — Question 67 | The subgroups of piecewise linear (PL for short) homeomorphisms of the line have been a rich source for interesting finitely generated groups with surprising algebraic and dynamical properties. However, not much is known about the algebraic properties of the PL homeomorphisms of higher dimensional PL manifolds. Althoug... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 67
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,127 | AMR-115-0068 | Foliations and Diffeomorphism Groups — Question 68 | It is likely that using Bowden-Hensel-Webb's work, one could show that ${\textnormal{\text{PL}}}_\circ(\Sigma,\text{rel }\partial)$ is not uniformly perfect for cases where $\text{Homeo}_0(\Sigma,\text{rel }\partial)$ is not uniformly perfect. This gives an h-principle approach for perfectness of ${\textnormal{\text{PL... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 68
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,128 | AMR-115-0069 | Foliations and Diffeomorphism Groups — Question 69 | Does an analog of discrete $\mathrm{GV}$ exist in higher dimensions? In particular, does there exist a $3$-cocycle in the third group cohomology $H^3(\mathrm{PL}_c(\mathbb{R}^2); \mathbb{R})$ that induces a surjection
\[
H_3(\mathrm{PL}_c(\mathbb{R}^2); \mathbb{Z})\twoheadrightarrow \mathbb{R}.
\] | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 69
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,129 | AMR-115-0070 | Foliations and Diffeomorphism Groups — Question 70 | Also, it is tempting to think about the analog of Milnor's conjecture for PL homeomorphisms. Recall that for a finite dimensional Lie group $G$, Milnor conjectured that
\[
H_*(BG^{\delta}; \mathbb{F}_p)\to H_*(BG; \mathbb{F}_p)
\]
is an isomorphism in all degrees. Here, $\mathbb{F}_p$ is the finite field with $p$ eleme... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 70
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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",
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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 |
800,130 | AMR-115-0071 | Foliations and Diffeomorphism Groups — Question 71 | As $B\Gamma_H$ has a trivial $\pi_2$ there is no nontrivial spherical cycle in
$H_2(B\Gamma_H; {\mathbb{Z}})$.
It is also known that all maps from the
2-torus $T^2$ to $B\Gamma_H$ yield trivial cycles in $H_2(B\Gamma_H; {\mathbb{Z}})$.
(Tsuboi [MR3726712]) Determine whether $H_2(B\Gamma_H;{\mathbb{Z}})=0$. | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 71
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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,
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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 |
800,131 | AMR-115-0072 | Foliations and Diffeomorphism Groups — Question 72 | If a loop in $B\Gamma_H$ is freely homotopic to one that is
transverse to the $\Gamma^\omega_1$ structure, it presents
a non trivial element in $\pi_1(B\overline{\Gamma}^\omega_1)=\Gamma_H$
which is of infinite order.
Does there exist a homotopically non-trivial loop in
$B\overline{\Gamma}^\omega_1$ which is not free-... | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 72
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,132 | AMR-115-0073 | Foliations and Diffeomorphism Groups — Question 73 | If this is not true, we can describe the whole $\Gamma_H$ fairly clearly,
but it is not plausible.
If it is true, we have a ${\mathbb{Z}}_{\geq 0}$-valued pseudonorm
on $\Gamma_H$.
Is the group $\Gamma_H$ simple? | Source list: Nariman, Yazdi - Problem List on Foliations and Diffeomorphism Groups (2025)
Source item: Question 73
Source URL: https://arxiv.org/abs/2503.18274
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Nariman, Yazdi | 2,025 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"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 |
800,133 | AMR-116-0001 | Comparative Prime Number Theory — Problem 1 | - (Greg Martin and Lior Silberman, University of British Columbia)
An *ordinate* of an $L$-function is a positive imaginary part of a nontrivial zero of that $L$-function. LI implies that at most one positive ordinate can be rational, and presumably even that is not possible (for classical analytic $L$-functions).
1}:... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#1)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,134 | AMR-116-0002 | Comparative Prime Number Theory — Problem 3 | One needs to be careful with higher-degree $L$-functions since there are known barriers to LI, such as: the factorization of Dedekind $\zeta$-functions and Artin $L$-functions into other $L$-functions; the vanishing of elliptic curve $L$-functions at the central point; and the ability to shift an entire $L$-function ve... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#3)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,135 | AMR-116-0003 | Comparative Prime Number Theory — Problem 4 | Can we obtain upper bounds for $1/{|\zeta'(\rho)|}$ as $\rho$ runs over the nontrivial zeros of $\zeta(s)$?
Assuming SZ for $\zeta(s)$, the Mertens sum has the explicit formula
\begin{equation*}
M_0(x) = \sum_\rho \frac{x^\rho}{\rho \zeta'(\rho)} -2 + \sum_{n= 1}^\infty \frac{(-1)^{n-1}(2\pi)^{2n}}{(2n)!n\zeta(2n+1)x^... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#4)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,136 | AMR-116-0004 | Comparative Prime Number Theory — Problem 5 | - (Nathan Ng, University of Lethbridge) My Ph.D. thesis [NgPhd] contains the conjecture
\[
\sum_{0 < \gamma < T} \biggl| \frac{\zeta(2 \rho)}{\zeta'(\rho)} \biggr|^2
\sim \frac{1}{2 \pi} T.
\]
**Problem 1**: Use the argument in Milinovich and Ng [MN] to establish
the lower bound
\[
\sum_{0 < \gamma < T} \biggl| \frac{\... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#5)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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,
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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 |
800,137 | AMR-116-0005 | Comparative Prime Number Theory — Problem 6 | Another example of a race with a large bias is the race between primes congruent to $2\mod3$ versus primes congruent to $1\mod3$. Rubinstein and Sarnak [RS] calculated the corresponding logarithmic density $\delta_{q;1,2} \approx 1.0\times10^{-3}$, while Bays and Hudson shows that the first sign change of $\pi(x;3,2) -... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#6)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,138 | AMR-116-0006 | Comparative Prime Number Theory — Problem 7 | Localize the first negative value for $\Delta_{\mathbb{K}}(x)$ when $\mathbb{K}$ is $\mathbb{Q}(\sqrt{5})$, $\mathbb{Q}(\sqrt{13})$, or some other simple number field. In general, obtain an upper bound for the first sign change of $\Delta_{\mathbb{K}}(x)$ for a family of number fields $\mathbb{K}$.
- (Alexandre Baille... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#7)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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,
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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 |
800,139 | AMR-116-0007 | Comparative Prime Number Theory — Problem 8 | More recently, Fiorilli and Jouve [FJ] and Bailleul [Bai] have investigated similar highly-biased races in number fields.
Bound Skewes's numbers of other highly biased races in terms of the parameters defining the race, either conjecturally or provably.
- (Alexandre Bailleul, Université Paris--Saclay) Consider Chebys... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#8)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,140 | AMR-116-0008 | Comparative Prime Number Theory — Problem 9 | - (Alexandre Bailleul, Université Paris--Saclay) Consider Chebyshev's bias in the function field setting. As is customary since the work of Cha [Cha], in addition to assuming the linear independence (over ${\mathbb{Q}}$) of the corresponding arguments of zeros of $L$-functions, one typically assumes that those argument... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#9)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,141 | AMR-116-0009 | Comparative Prime Number Theory — Problem 10 | - (Stanley Yao Xiao, University of Northern British Columbia)
Let $f \in \mathbb{Z}[x,y]$ be a primitive, positive definite binary quadratic form such that $f(x,1) \not \equiv x(x+1) \pmod{2}$. Consider the counting function for the generalized Friedlander--Iwaniec primes
\[
\pi_f(x) = \# \{p \leq x \colon p = f(a,b^2)... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#10)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,142 | AMR-116-0010 | Comparative Prime Number Theory — Problem 11 | - (Greg Martin, University of British Columbia)
This question was asked by Carl Pomerance and appears in [Mar, Section 3]. Let $a$ and $b$ be distinct reduced residue classes modulo $q$.
Prove unconditionally that the set of $x$ for which $\pi(x;q,a)=\pi(x;q,b)$ (the set of ``ties'' in the prime number race) has (natu... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#11)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
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"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"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 |
800,143 | AMR-116-0011 | Comparative Prime Number Theory — Problem 12 | - (Daniel R. Johnston, University of New South Wales--Canberra at ADFA)
Define
\[
S(x)=\sum_{n\leq x}(-2)^{\Omega(n)}
\qquad\text{and}\qquad
\alpha = \limsup_{x\to\infty}\frac{|S(x)|}{x}.
\]
In a soon-to-be-released preprint by students at UNSW--Canberra, it is shown that $\alpha$ exists, and a (large) upper bound is g... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#12)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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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800,144 | AMR-116-0012 | Comparative Prime Number Theory — Problem 1 | The best improvement to this lower bound I am aware of is by Morrill, Platt, and Trudgian [MPT] (improving work of Kaczorowski [K2]), who proved that
\[
\liminf \frac{W^\psi(T)}{\log T} \ge \frac{\gamma_1}{\pi} + 1.867\cdot10^{-30}.
\]
Improve this lower bound, even assuming RH. Here are some suggested target lower bo... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem 1 (#13)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
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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 |
800,145 | AMR-116-0013 | Comparative Prime Number Theory — Problem 2 | What we expect to be true is that the large-scale intervals of positive and negative values of $\psi(x)-x$ do indeed alternate at about the speed given by the repeated-averaging argument, but that each such sign change detected is actually a flurry of many sign changes on a small scale (this is how random walks behave,... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem 2 (#14)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"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"
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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 |
800,146 | AMR-116-0014 | Comparative Prime Number Theory — Problem 15 | - (Alexandre Bailleul, Université Paris--Saclay) This question was raised by Nilotpal Sinha [Sinha]. Let $P^+(n)$ denote the largest prime factor of $n$. Numerical investigation suggests that there is a bias towards integers $n$ for which $P^+(n)\equiv3\mod4$ over integers $n$ for which $P^+(n)\equiv1\mod4$, but the as... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#15)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,147 | AMR-116-0015 | Comparative Prime Number Theory — Problem 1 | - (Nathan Ng, University of Lethbridge)
Feuerverger and Martin [FeM] numerically computed the densities for some three-way races, as well as for the four-way races for the moduli $5$, $8$, and $12$. Their paper contains a general formula for densities in races with any number of competitors; but there have been few (if... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem 1 (#16)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,148 | AMR-116-0016 | Comparative Prime Number Theory — Problem 2 | **Problem 1**: Numerically compute some further three-way (or higher) races.
Fiorilli and Martin [FiM] determined the 117 most biased two-way races.
Determine the $100$ (for example) most biased three-way races.
It could be more challenging to bound the densities in three-way races sufficiently well to verify that s... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem 2 (#17)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,149 | AMR-116-0017 | Comparative Prime Number Theory — Problem 18 | It could be more challenging to bound the densities in three-way races sufficiently well to verify that such a list is exhaustive: as Lamzouri [Lam] showed, the rate of convergence of three-way race densities to $\frac16$ is only $O(1/\log q)$, as opposed to a $q^{-1/2+o(1)}$ rate of convergence to $\frac12$ for densit... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#18)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,150 | AMR-116-0018 | Comparative Prime Number Theory — Problem 19 | Investigate further examples. Determine the most biased two-way Chebotarev races.
- (Greg Martin, University of British Columbia)
In 1959 Shanks [Shanks] made an observation that seems to have been overlooked since then: some combinatorial reasoning led him to assert that for each integer $k\ge1$, the odd numbers $n$ ... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#19)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,151 | AMR-116-0019 | Comparative Prime Number Theory — Problem 20 | - (Greg Martin, University of British Columbia)
In 1959 Shanks [Shanks] made an observation that seems to have been overlooked since then: some combinatorial reasoning led him to assert that for each integer $k\ge1$, the odd numbers $n$ with $\Omega(n)=k$ should be biased towards the residue class $(-1)^k\mod4$, where ... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#20)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,152 | AMR-116-0020 | Comparative Prime Number Theory — Problem 21 | - (Daniel R. Johnston, University of New South Wales--Canberra at ADFA).
It has been shown [johnston2023average, Theorem 1.1] that RH is equivalent to
\[
{\mathfrak{A}}_1^\pi(x) = \int_0^x \bigl( \pi(t)-\mathop\mathrm{li}(t) \bigr) dt < 0 \quad\text{for all $x>2$.}
\]
Roughly, the reason this inequality holds under RH ... | Source list: Hamieh, Kadiri, Martin, Ng - Comparative Prime Number Theory Problem List (2024)
Source item: Problem (#21)
Source URL: https://arxiv.org/abs/2407.03530
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Martin, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,153 | AMR-117-0001 | Moments of L-functions — Moments of the Riemann zeta function — Problem 1 | Give an explicit version of Harper's [Ha] upper bound for $I_k(T)$, assuming the Riemann hypothesis. That is, for $k >0$ determine $C_k$ such that
\begin{equation}
I_k(T) \le C_k T (\log T)^{k^2}
\end{equation}
for $T$ sufficiently large.
Note that this is related to the following conjecture of Soundararajan [S2]
for ... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,154 | AMR-117-0002 | Moments of L-functions — Moments of the Riemann zeta function — Problem 3 | We have also been informed a graduate student has worked extensively on this problem and nearly has a result. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,155 | AMR-117-0003 | Moments of L-functions — Moments of the Riemann zeta function — Problem 4 | Smoothed fourth moment. Let $\omega(t)$ be a smooth compactly supported function supported in $[c_1T, c_2T]$ where $0 < c_1 < c_2$.
Show that
\[
\int_{-\infty}^{\infty} \omega(t) |\zeta(\tfrac{1}{2}+i t)|^{4} dt = O(T^{\frac{1}{2} + \theta+\varepsilon })
\]
where
$\theta$ is upper
bound in Ramanujan's conjecture.
See [... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,156 | AMR-117-0004 | Moments of L-functions — Moments of the Riemann zeta function — Problem 5 | In 1989 Zavorotnyi proved that
\[
I_2(T) = T P_4 (\log T) + O( T^{\frac{2}{3}+\varepsilon}),
\]
where $P_4$ is a specific degree $4$ polynomial.
Improve the bound in the error term. \\
(Nathan Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 5
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,157 | AMR-117-0005 | Moments of L-functions — Moments of the Riemann zeta function — Problem 6 | Conrey *el al* made the conjecture
\[
I_k(T) = TP_{k^2} (\log T) + O(T^{\frac{1}{2} + \varepsilon})
\]
where $P_{k^2}$ is a certain degree $k^2$ polynomial. Let
\[
E_k(T) = I_k(T) -TP_{k^2} (\log T)
\]
denote the error term. Since the publication of [CFKRS] there has been some debate on what should be the correct
conje... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 6
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,158 | AMR-117-0006 | Moments of L-functions — Moments of the Riemann zeta function — Problem 7 | Improve Chandee's [Ch, Theorem 1.2].
\begin{theorem}
Let $k_i$ be positive real numbers. Let $\alpha_i=\alpha_i(T)$ be real-valued functions of $T$ such that $\alpha_i =o(T)$. Assume that $\lim_{T\rightarrow \infty} \alpha_i\log T$ and $\lim_{T\rightarrow \infty} (\alpha_i-\alpha_j)\log T$ exist or equal $\pm \infty$. ... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 7
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,159 | AMR-117-0007 | Moments of L-functions — Moments of the Riemann zeta function — Problem 9 | Soundararajan [S] proved the following lower bound for $I_3(T)$:
\[
I_3(T) \ge \frac{20.26 a_3}{9!} (1+o(1)) T (\log T)^9,
\]
for $T$ sufficiently large. Improve the value of 20.26. The best possible result would be 42.
(Likewise improve the lower bounds for $I_k(T)$ for $k >3$.) Note that the works [BBLR], [BCR], and ... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 9
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,160 | AMR-117-0008 | Moments of L-functions — Moments of the Riemann zeta function — Problem 10 | We have been informed a graduate student has worked extensively on this problem and nearly has a result. | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 10
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,161 | AMR-117-0009 | Moments of L-functions — Moments of the Riemann zeta function — Problem 11 | Is it possible to prove an omega theorem for $I_3(T)$ assuming the ternary additive divisor conjecture?
Prove that there exists $\Theta >0$, such that
\[
I_3(T) = T \mathcal{P}_9(\log T) + \Omega(T^{\Theta})
\]
where $\mathcal{P}_9$ is a certain degree nine polynomial. \\
(Nathan Ng, Lethbridge) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 11
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,162 | AMR-117-0010 | Moments of L-functions — Moments of the Riemann zeta function — Problem 12 | Ng, Shen, and Wong [NSW] showed that the Riemann hypothesis and a smoothed quaternary additive divisor conjecture imply
the conjectured asymptotic
\[
I_4(T) \sim C_4 T (\log T)^{16}
\]
for a certain positive constant $C_4$. Under the same assumptions, obtain the full main term, up to an error term of size $o(T)$ or a p... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 12
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,163 | AMR-117-0011 | Moments of L-functions — Moments of the Riemann zeta function — Problem 13 | In [CFKRS] a conjectural method known as the `recipe' is introduced. The `recipe' was used to produce (conjecturally) a full asymptotic formula for $I_k(T)$.
Can the `recipe' be made rigorous in the case of the fourth moment? That is, can we give a new proof of the asymptotic formula with power savings error term for $... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 13
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,164 | AMR-117-0012 | Moments of L-functions — Moments of the Riemann zeta function — Problem 14 | Can the conjectural lower order terms for $I_k(T)$ (due to CFKRS [CFKRS] and Diaconu-Goldfeld-Hoffstein [DGH]) be recovered by refining the splitting conjecture in the Gonek-Hughes-Keating [GHK] hybrid Euler-Hadamard product? \\
(Anurag Sahay, Rochester) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 14
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,165 | AMR-117-0013 | Moments of L-functions — Moments of the Riemann zeta function — Problem 15 | Prove third and fourth moment asymptotics with best possible error terms for $L(1/2,f)$ as $f$ runs over holomorphic Hecke eigenforms of weight $k_f \leq T$. It should be possible to show, using current technology, that
\[\sum_{k_f \leq T} \frac{L\left(\frac{1}{2},f\right)^3}{L(1,\operatorname{ad}f)} = T^2 P_3(\log T) ... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 15
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,166 | AMR-117-0014 | Moments of L-functions — Moments of the Riemann zeta function — Problem 16 | Heath-Brown proved the famous Weyl-strength twelfth moment bound
\[\int_{0}^{T} \left|\zeta\left(\frac{1}{2}+it\right)\right|^{12} dt \ll_{\varepsilon} T^{2 + \varepsilon}\]
for the Riemann zeta function. Jutila generalised this to prove an analogous result for the sixth moment in the $t$-aspect of $L(1/2 + it,f)$, whe... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 16
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,167 | AMR-117-0015 | Moments of L-functions — Moments of the Riemann zeta function — Problem 17 | Jutila proved the Weyl-strength twelfth moment bound
\[\sum_{t_f \leq T} \frac{L\left(\frac{1}{2},f\right)^{12}}{L(1,\operatorname{ad}f)} \ll_{\varepsilon} T^{4 + \varepsilon},\]
where the sum is over Hecke--Maass cusp forms of level 1 and spectral parameter at most $T$. Can one prove a level-aspect analogue of this, w... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 17
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,168 | AMR-117-0016 | Moments of L-functions — Moments of the Riemann zeta function — Problem 18 | Good showed that given a Hecke--Maass cusp form of level 1 and fixed spectral parameter $t_f$, we have that
\[\int_{0}^{T} \left|L\left(\frac{1}{2}+it,f\right)\right|^2 dt = T P_1(\log T) + O_{t_f,\varepsilon}(T^{2/3 + \varepsilon}),\]
where $P_1(x)$ denotes some polynomial of degree 1 in x. Crucially, the dependence o... | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 18
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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 |
800,169 | AMR-117-0017 | Moments of L-functions — Moments of the Riemann zeta function — Problem 19 | Use the recent work of Humphries-Khan [HK] to compute weight aspect upper bounds for the 6th moment of $L(\frac12,f\otimes g)$ where $f$ and $g$ vary over the set of primitive forms of level 1 and weights $k$ and $\ell$ respectively, with $|k-\ell|=O(1)$ and $K<k+\ell\leq2K$.\\
(Alia Hamieh, UNBC) | Source list: Hamieh, Kadiri, Ng - Moments of L-functions Problem List (2024)
Source item: Problem 19
Source URL: https://arxiv.org/abs/2405.17800
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Hamieh, Kadiri, Ng | 2,024 | 1 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"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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