Updated on 2024/04/03

写真a

 
MATSUZAWA YOSUKE
 
Organization
Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics
Title
Associate Professor
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 ）

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

  • Preimages question of self-morphisms on projective varieties

    2023   9 - 13   2024.01

  • 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 ）

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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 ）

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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 ）

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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 ）

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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 ）

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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 ）

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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

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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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Social Activities

  • 関西科学塾

    Role(s)： Lecturer

    関西科学塾  2023.10

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    Type：Visiting lecture