Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

We propose a stochastic process of interacting many agents, which is inspired by rank-based supplanting dynamics commonly observed in a group of Japanese macaques. In order to characterize the breaking of permutation symmetry with respect to agents' rank in the stochastic process, we introduce a rank-dependent quantity, overlap centrality, which quantifies how often a given agent overlaps with the other agents. We give a sufficient condition in a wide class of the models such that overlap centrality shows perfect correlation in terms of the agents' rank in the zero-supplanting limit. We also discuss a singularity of the correlation in the case of interaction induced by a Potts energy.

DOI： 10.1103/PhysRevE.107.034114

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.107.034114/fulltext

Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

We study the finiteness of low degree points on certain modular curves and their Atkin–Lehner quotients, and, as an application, prove the modularity of elliptic curves over all but finitely many totally real fields of degree 5. On the way, we prove a criterion for the finiteness of rational points of degree 5 on a curve of large genus over a number field using the results of Abramovich–Harris and Faltings on subvarieties of Jacobians.

DOI： 10.1007/s40993-022-00383-0

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Other Link： https://link.springer.com/article/10.1007/s40993-022-00383-0/fulltext.html

Language：English   Publishing type：Research paper (scientific journal)  

We use explicit methods to study the [Formula: see text]-torsion points on the Jacobian variety of the Fermat quartic. With the aid of computer algebra systems, we explicitly give a basis of the group of [Formula: see text]-torsion points. We calculate the Galois action, and show that the image of the mod [Formula: see text] Galois representation is isomorphic to the dihedral group of order [Formula: see text]. As applications, we calculate the Mordell–Weil group of the Jacobian variety of the Fermat quartic over each subfield of the [Formula: see text]th cyclotomic field. We determine all of the points on the Fermat quartic defined over quadratic extensions of the [Formula: see text]th cyclotomic field. Thus, we complete Faddeev’s work in 1960.

DOI： 10.1142/s1793042120500451

Language：English   Publishing type：Research paper (scientific journal)  

Can a smooth plane cubic be defined by the determinant of a square matrix with entries in linear forms in three variables? If we can, we say that it admits a linear determinantal representation. In this paper, we investigate linear determinantal representations of smooth plane cubics over various fields, and prove that any smooth plane cubic over a large field (or an ample field) admits a linear determinantal representation. Since local fields are large, any smooth plane cubic over a local field always admits a linear determinantal representation. As an application, we prove that a positive proportion of smooth plane cubics over Q, ordered by height, admit linear determinantal representations. We also prove that, if the conjecture of Bhargava–Kane–Lenstra–Poonen–Rains on the distribution of Selmer groups is true, a positive proportion of smooth plane cubics over Q fail the local-global principle for the existence of linear determinantal representations.

Repository Public URL： https://hdl.handle.net/2324/7174349

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Public Library of Science (PLoS)  

Human T-cell leukemia virus type 1 (HTLV-1) causes adult T-cell leukemia (ATL) and HTLV-1-associated myelopathy (HAM) after a long latent period in a fraction of infected individuals. These HTLV-1-infected cells typically have phenotypes similar to that of CD4⁺T cells, but the cell status is not well understood. To extract the inherent information of HTLV-1-infected CD4⁺ cells, we integratively analyzed the ATAC-seq and RNA-seq data of the infected cells. Compared to CD4⁺T cells from healthy donors, we found anomalous chromatin accessibility in HTLV-1infected CD4⁺ cells derived from ATL cases in terms of location and sample-to-sample fluctuations in open chromatin regions. Further, by focusing on systematically selected genes near the open chromatin regions, we quantified the difference between the infected CD4⁺ cells in ATL cases and healthy CD4⁺T cells in terms of the correlation between the chromatin structures and the gene expressions. Based on a further analysis of chromatin accessibility, we detected TLL1 (Tolloid Like 1) as one of the key genes that exhibit unique gene expressions in ATL cases. A luciferase assay indicated that TLL1 has an isoform-dependent regulatory effect on TGF-β. Overall, this study provides results about the status of HTLV-1-infected cells, which are qualitatively consistent across the different scales of chromatin accessibility, transcription, and immunophenotype.

DOI： 10.1371/journal.pcbi.1012690

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Event date： 2023.10

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：RIMS, Kyoto University   Country：Japan  

Exponential sums on binary quartic forms and its applications

Event date： 2024.7

Language：English   Presentation type：Oral presentation (general)  

Venue：Massachusetts Institute of Technology   Country：United States  

Event date： 2023.12

Language：English   Presentation type：Oral presentation (general)  

Venue：九州大学   Country：Japan  

Event date： 2023.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Kobe University   Country：Japan  

In 2014, Bhargava proved that a positive proportion of genus one curves defined by integral binary quartics have Q-rational points. Recently, Bhargava and Ho studied the case when we restrict curves to a family of binary quartics. In this talk, I will explain results on another family related to congruent numbers. This is a joint work with Yoshinori Kanamura (Keio University).

Event date： 2022.3

Language：Japanese  

Venue：オンライン   Country：Japan  

We investigate exponential sums over singular binary quartic forms, proving
an explicit formula for the finite field Fourier transform of this set. Our
formula shares much in common with analogous formulas proved previously for
other vector spaces, but also exhibits a striking new feature: the point
counting function $a_p(E) = p + 1 - \#E(\mathbb{F}_p)$ associated to an
associated elliptic curve makes a prominent appearance. The proof techniques
are also new, involving techniques from elementary algebraic geometry and
classical invariant theory. As an application to prime number theory, we
demonstrate the existence of `many' 2-Selmer elements for elliptic curves with
discriminants that are squarefree and have at most four prime factors.

arXiv

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Other Link： http://arxiv.org/pdf/2404.00541v1

We study an integer sequence associated with Cantor's division polynomials of
a genus 2 curve having an integral point. We show that the reduction modulo $p$
of such a sequence is periodic for all but finitely many primes $p$, and
describe the relation between the period of the reduction modulo $p$ of the
sequence and the order of the integral point on the reduction modulo $p$ in the
Jacobian variety explicitly. This generalizes Ward's results on elliptic
divisibility sequences associated with division polynomials of elliptic curves.

arXiv

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Other Link： http://arxiv.org/pdf/2310.01013v2

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

Type：Peer review 

Number of peer-reviewed articles in foreign language journals：1

大阪市科学館の発行する「月刊うちゅう」に、数学の解説記事を寄稿した。内容は十進法を始めとする数の表記の一般化についてというもので、主に中学生を対象として「数学は教科書の内容からどう発展していくのか」を追体験することを目的としたものである。