Researcher Profiles - MATSUZAWA YOSUKE

写真a

MATSUZAWA YOSUKE

Organization

Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics

Affiliation

Institute of Science

Homepage

https://sites.google.com/brown.edu/yohsukematsuzawa/home

Affiliation campus

Sugimoto Campus

Position

Graduate School of Science Department of Mathematics

Associate Professor 2022.10 - Now
School of Science Department of Mathematics

Associate Professor 2022.10 - Now

Degree

数理科学博士（ The University of Tokyo ）
数理科学修士（ The University of Tokyo ）
理学学士（ The University of Tokyo ）

Awards

科学技術分野の文部科学大臣表彰若手科学者賞

2024.04 文部科学省ディオファントス幾何からの視点による数論力学系の研究

Job Career (off-campus)

Osaka Metropolitan University Department of Mathematics

2022.10 - Now
Rikkyo University

2021.04 - 2022.09
Brown University Department of Mathematics Visiting assistant professor

2019.09 - 2021.03
The University of Tokyo Graduate School of Mathematical Sciences

2019.04 - 2019.09

Papers

Unified total body CT image with multiple organ specific windowings: validating improved diagnostic accuracy and speed in trauma cases

Okada N.

Scientific Reports 15 ( 1 ) 5654 2025.12

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DOI： 10.1038/s41598-024-83346-y

PubMed
Arithmetic degrees and Zariski dense orbits of cohomologically hyperbolic maps Reviewed

Yohsuke Matsuzawa, Long Wang

Transactions of the American Mathematical Society 377 ( 9 ) 6311 - 6340 2024.06（ ISSN:0002-9947 ）（ eISSN:1088-6850 ）

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Publishing type：Research paper (scientific journal)

<p>A dominant rational self-map on a projective variety is called -cohomologically hyperbolic if the -th dynamical degree is strictly larger than other dynamical degrees. For such a map defined over , we study lower bounds of the arithmetic degrees, existence of points with Zariski dense orbit, and finiteness of preperiodic points. In particular, we prove that, if is an -cohomologically hyperbolic map on a smooth projective variety, then (1) the arithmetic degree of a -point with generic -orbit is equal to the first dynamical degree of ; and (2) there are -points with generic -orbit. Applying our theorem to the recently constructed rational map with transcendental dynamical degree, we confirm that the arithmetic degree can be transcendental.</p>

DOI： 10.1090/tran/9211

Other URL： https://www.ams.org/tran/0000-000-00/S0002-9947-2024-09211-5/S0002-9947-2024-09211-5.pdf
Preimages question of self-morphisms on projective varieties

2023 9 - 13 2024.01
Recent advances on Kawaguchi-Silverman conjecture Reviewed

松澤陽介

Proceedings for the Simons Symposia on Algebraic, Complex, and Arithmetic Dynamics - 2024
Non-density of Points of Small Arithmetic Degrees Reviewed

Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata, De-Qi Zhang

The Journal of Geometric Analysis 33 ( 4 ) 2023.02（ ISSN:1050-6926 ）（ eISSN:1559-002X ）

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Publishing type：Research paper (scientific journal)

DOI： 10.1007/s12220-022-01156-y

Other URL： https://link.springer.com/article/10.1007/s12220-022-01156-y/fulltext.html
On Dynamical Cancellation Reviewed

Jason P Bell, Yohsuke Matsuzawa, Matthew Satriano

International Mathematics Research Notices 2023 ( 8 ) 7099 - 7139 2022.03（ ISSN:1073-7928 ）（ eISSN:1687-0247 ）

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Publishing type：Research paper (scientific journal)

Abstract

Let $X$ be a projective variety and let $f$ be a dominant endomorphism of $X$, both of which are defined over a number field $K$. We consider a question of the 2nd author, Meng, Shibata, and Zhang, who asks whether the tower of $K$-points $Y(K)\subseteq (f^{-1}(Y))(K)\subseteq (f^{-2}(Y))(K)\subseteq \cdots $ eventually stabilizes, where $Y\subset X$ is a subvariety invariant under $f$. We show this question has an affirmative answer when the map $f$ is étale. We also look at a related problem of showing that there is some integer $s_0$, depending only on $X$ and $K$, such that whenever $x, y \in X(K)$ have the property that $f^{s}(x) = f^{s}(y)$ for some $s \geqslant 0$, we necessarily have $f^{s_{0 } }(x) = f^{s_{0 } }(y)$. We prove this holds for étale morphisms of projective varieties, as well as self-morphisms of smooth projective curves. We also prove a more general cancellation theorem for polynomial maps on ${\mathbb {P } }^1$ where we allow for composition by multiple different maps $f_1,\dots ,f_r$.

DOI： 10.1093/imrn/rnac058
Kawaguchi–Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism Reviewed

Yohsuke Matsuzawa, Shou Yoshikawa

Mathematische Annalen 2021.11（ ISSN:0025-5831 ）（ eISSN:1432-1807 ）

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Publishing type：Research paper (scientific journal)

DOI： 10.1007/s00208-021-02305-4

Other URL： https://link.springer.com/article/10.1007/s00208-021-02305-4/fulltext.html
The distribution relation and inverse function theorem in arithmetic geometry Reviewed

Yohsuke Matsuzawa, Joseph H. Silverman

Journal of Number Theory 226 307 - 357 2021.09（ ISSN:0022-314X ）

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Publishing type：Research paper (scientific journal)

DOI： 10.1016/j.jnt.2021.03.016
A note on Kawaguchi–Silverman conjecture Reviewed

Sichen Li, Yohsuke Matsuzawa

International Journal of Mathematics 2150085 - 2150085 2021.08（ ISSN:0129-167X ）（ eISSN:1793-6519 ）

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Publishing type：Research paper (scientific journal)

We collect some results on endomorphisms on projective varieties related to the Kawaguchi–Silverman conjecture. We discuss certain conditions on automorphism groups of projective varieties and positivity conditions on leading real eigendivisors of self-morphisms. We prove Kawaguchi–Silverman conjecture for endomorphisms on projective bundles on a smooth Fano variety of Picard number one. In the last section, we discuss endomorphisms and augmented base loci of their eigendivisors.

DOI： 10.1142/s0129167x21500853
Int-amplified Endomorphisms on Normal Projective Surfaces Reviewed

Yohsuke Matsuzawa, Shou Yoshikawa

Taiwanese Journal of Mathematics 25 ( 4 ) 2021.07（ ISSN:1027-5487 ）

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Publishing type：Research paper (scientific journal)

DOI： 10.11650/tjm/210101
Invariant Subvarieties With Small Dynamical Degree Reviewed

Yohsuke Matsuzawa, Sheng Meng, Takahiro Shibata, De-Qi Zhang, Guolei Zhong

International Mathematics Research Notices 2022 ( 15 ) 11448 - 11483 2021.04（ ISSN:1073-7928 ）（ eISSN:1687-0247 ）

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Publishing type：Research paper (scientific journal)

Abstract

Let $f:X\to X $ be a dominant self-morphism of an algebraic variety. Consider the set $\Sigma _{f^{\infty } }$ of $f$-periodic subvarieties of small dynamical degree (SDD), the subset $S_{f^{\infty } }$ of maximal elements in $\Sigma _{f^{\infty } }$, and the subset $S_f$ of $f$-invariant elements in $S_{f^{\infty } }$. When $X$ is projective, we prove the finiteness of the set $P_f$ of $f$-invariant prime divisors with SDD and give an optimal upper bound $$\begin{align*} &\sharp P_{f^n}\le d_1(f)^n(1+o(1))\end{align*}$$as $n\to \infty $, where $d_1(f)$ is the 1st dynamic degree. When $X$ is an algebraic group (with $f$ being a translation of an isogeny), or a (not necessarily complete) toric variety, we give an optimal upper bound $$\begin{align*} &\sharp S_{f^n}\le d_1(f)^{n\cdot\dim(X)}(1+o(1))\end{align*}$$as $n \to \infty $, which slightly generalizes a conjecture of S.-W. Zhang for polarized $f$.

DOI： 10.1093/imrn/rnab039
Growth of local height functions along orbits of self-morphisms on projective varieties Reviewed

Yohsuke Matsuzawa

Int. Math. Res. Not. IMR 2021

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Publishing type：Research paper (scientific journal)
Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties Reviewed

YOHSUKE MATSUZAWA, KAORU SANO

Ergodic Theory and Dynamical Systems 40 ( 6 ) 1655 - 1672 2020.06（ ISSN:0143-3857 ）（ eISSN:1469-4417 ）

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Publishing type：Research paper (scientific journal)

We prove a conjecture by Kawaguchi–Silverman on arithmetic and dynamical degrees, for self-morphisms of semi-abelian varieties. Moreover, we determine the set of the arithmetic degrees of orbits and the (first) dynamical degrees of self-morphisms of semi-abelian varieties.

DOI： 10.1017/etds.2018.117
Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties Reviewed

Yohsuke Matsuzawa

Advances in Mathematics 366 107086 - 107086 2020.06（ ISSN:0001-8708 ）

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Publishing type：Research paper (scientific journal)

DOI： 10.1016/j.aim.2020.107086
Arithmetic and dynamical degrees of rational self-maps on algebraic varieties (Algebraic Number Theory and Related Topics 2016) Reviewed

Yohsuke Matsuzawa

RIMS Kˆokyuˆroku Bessatsu B77 183 - 189 2020.04
On upper bounds of arithmetic degrees Reviewed

Yohsuke Matsuzawa

American Journal of Mathematics 142 ( 6 ) 1797 - 1875 2020（ eISSN:1080-6377 ）

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Publishing type：Research paper (scientific journal)

DOI： 10.1353/ajm.2020.0045

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Presentations

Preimages question of self-morphisms on projective varieties Invited International conference

Workshop on Nonarchimedean Geometry and Related Fields 2024.02
Preimages question of self-morphisms on projective varieties over number fields Invited Domestic conference

2024.01
Arithmetic dynamics on algebraic varieties Invited Domestic conference

2024.01
Preimages question of self-morphisms on projective varieties over number fields Invited Domestic conference

2023.11
Preimages question of self-morphisms on projective varieties Invited International conference

2023.10
高次元数論力学系の諸問題 Invited Domestic conference

松澤陽介

代数学シンポジウム 2023.08
数論力学系の紹介 Invited Domestic conference

松澤陽介

NTT 基礎数学セミナー 2023.04

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Grant-in-Aid for Scientific Research

代数多様体の数論力学系の研究

Grant-in-Aid for Early-Career Scientists 2026
代数多様体の数論力学系の研究

Grant-in-Aid for Early-Career Scientists 2025
代数多様体の数論力学系の研究

Grant-in-Aid for Early-Career Scientists 2024

Charge of on-campus class subject

数学特別研究2A

2024 Intensive lecture Graduate school
数学特別研究1A

2024 Intensive lecture Graduate school
数理構造論演習1

2024 Intensive lecture Graduate school
数理科学A

2024 Weekly class Graduate school
数学特別研究3A

2024 Intensive lecture Graduate school
数学特別研究5A

2024 Intensive lecture Graduate school
数学特別研究4A

2024 Intensive lecture Graduate school
線形代数1

2024 Weekly class Graduate school
数学特別研究2B

2024 Intensive lecture Graduate school
数学特別研究1B

2024 Intensive lecture Graduate school
海外特別研究2

2024 Intensive lecture Graduate school
海外特別研究2

2024 Intensive lecture Graduate school
海外特別研究1

2024 Intensive lecture Graduate school
数理解析学演習1

2024 Intensive lecture Graduate school
数理構造論演習2

2024 Intensive lecture Graduate school
数理構造論演習2

2024 Intensive lecture Graduate school
数理構造論特別講義A

2024 Intensive lecture Graduate school
数学特別研究5B

2024 Intensive lecture Graduate school
数学特別研究4B

2024 Intensive lecture Graduate school
数学特別研究3B

2024 Intensive lecture Graduate school
海外特別研究5

2024 Intensive lecture Graduate school
海外特別研究4

2024 Intensive lecture Graduate school
海外特別研究3

2024 Intensive lecture Graduate school
数理解析学ゼミナールA

2024 Intensive lecture Graduate school
線形代数2A

2024 Weekly class Graduate school
微積分2

2024 Weekly class Graduate school
基礎数学B

2024 Weekly class Graduate school
特別研究

2024 Intensive lecture Undergraduate
海外特別研究

2024 Intensive lecture Undergraduate

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Social Activities　⇒ Link to the list of Social Activities

関西科学塾

Role(s)： Lecturer

Type： Visiting lecture

関西科学塾 2023.10

Position

Position

Degree

Degree

Awards

Awards

Job Career (off-campus)

Job Career (off-campus)

Papers

Papers

Presentations

Presentations

Grant-in-Aid for Scientific Research

Grant-in-Aid for Scientific Research

Charge of on-campus class subject

Charge of on-campus class subject

Social Activities ⇒ Link to the list of Social Activities

Social Activities ⇒ Link to the list of Social Activities

Social Activities　⇒ Link to the list of Social Activities

Social Activities　⇒ Link to the list of Social Activities