Izeki, Hiroyasu

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics ( Yagami )

Position

Professor

E-mail Address

E-mail address

Scopus Paper Info  
Paper Count: 14 Citation Count: 118 h-index: 6

Click to view the Scopus page. The data was downloaded from Scopus API in May 24, 2026, via http://api.elsevier.com and http://www.scopus.com .

Page Top ▲

Career 【 Display / hide 】

  • 1992.04
    -
    1995.03

    東京都立大学, 理学部, 助手

  • 1995.04
    -
    1997.03

    名古屋大学大学院, 多元数理科学研究科, 助教授

  • 1997.04
    -
    2007.03

    東北大学大学院, 理学研究科, 助教授

  • 2007.04
    -
    2010.03

    東北大学大学院, 理学研究科, 准教授

  • 2010.04
    -
    Present

    慶應義塾大学, 理工学部, 教授

display all >>

Page Top ▲

Academic Background 【 Display / hide 】

  • 1989.03

    Keio University, Faculty of Science and Engineering, 数理科学科・数学専攻

    University, Graduated

  • 1991.03

    Keio University, Graduate School, Division of Science and Engineering, 数理科学専攻

    Graduate School, Completed, Master's course

Page Top ▲

Academic Degrees 【 Display / hide 】

  • 博士（理学）, Keio University, Dissertation, 1994.12

Page Top ▲
 

Research Areas 【 Display / hide 】

  • Natural Science / Geometry

Page Top ▲

Research Keywords 【 Display / hide 】

  • rigidity

  • fixed-point property

  • finitely generated group

  • harmonic map

  • nonpositively curved space

Page Top ▲

Research Themes 【 Display / hide 】

  • rigidity and fixed-point property of discrete groups, 

    2003
    -
    Present

Page Top ▲
 

Books 【 Display / hide 】

  • Yamabe Problem

    Osamu Kobayashi, Kazuo Akutagawa, IZEKI Hiroyasu, Mathematical Society of Japan, 2013.12

    Scope: Chapter 9

  • 文科系のための自然科学総合実験

    IZEKI Hiroyasu, 2008.03

    Scope: 163-173

  • 数学事典 第４版

    IZEKI Hiroyasu, NAYATANI Shin, 2007.03

    Scope: 252-255

  • 21世紀の数学 --- 幾何学の未踏峰

    IZEKI Hiroyasu, 2004.07

    Scope: 168-182

Page Top ▲

Papers 【 Display / hide 】

  • Torsion groups of subexponential growth cannot act on finite-dimensional CAT(0)-spaces without a fixed point

    Hiroyasu Izeki, Anders Karlsson

    Commentarii Mathematici Helvetici (EMS Press)   2026.04

    Research paper (scientific journal), Joint Work, Accepted

    　View Summary

    We show that finitely generated groups which are Liouville and without infinite finite-dimensional linear representations must have a global fixed point whenever they act by isometry on a finite-dimensional complete CAT(0)-space. This provides a partial answer to an old question in geometric group theory and proves partly a conjecture formulated by Norin, Osajda, and Przytycki. It applies in particular to Grigorchuk's groups of intermediate growth and other branch groups as well as to simple groups with the Liouville property such as those found by Matte Bon and by Nekrashevych. The method of proof uses ultralimits, equivariant harmonic maps, subharmonic functions, horofunctions and random walks.

  • A CAT(0) alternative for amenable groups and a Kazhdan-type rigidity principle

    Hiroyasu Izeki, Ran Ji, Anders Karlsson, Yunhui Wu

     2026.03

    　View Summary

    We prove that finitely generated amenable groups acting on CAT(0) spaces satisfy the following alternative: either every action on a geodesically complete CAT(0) space with bounded geometry (or finite dimension) has a global fixed point, or the group admits a fixed-point-free action on $\mathbb{R}^n$. As a consequence, finitely generated amenable torsion groups and finitely generated virtually simple amenable groups cannot act nontrivially on geodesically complete CAT(0) spaces with bounded geometry or on finite-dimensional complete CAT(0) spaces.
    The proof relies on a Kazhdan-type rigidity theorem for groups with the Euclidean fixed point property: if such a group acts on a geodesically complete CAT(0) space of bounded geometry with almost fixed points, then it has a genuine fixed point. This yields several further corollaries, including a rigidity dichotomy for drift and that any finitely generated torsion group acting on a geodesically complete visibility CAT(0) space with bounded geometry must have a global fixed point. These results make substantial progress on the longstanding problem of understanding actions of torsion groups on CAT(0) spaces.

  • Isometric group actions with vanishing rate of escape on CAT(0) spaces

    Hiroyasu Izeki

    Geom. Funct. Anal.  33 ( 1 ) 170 - 244 2023.01

    Research paper (scientific journal), Single Work, Accepted

  • A fixed point property of random groups

    IZEKI Hiroyasu

    京都大学数理解析研究所講究録  2018.04

    Research paper (conference, symposium, etc.), Single Work

  • Poisson boundary and rigidity of discrete groups

    IZEKI Hiroyasu

    Geometry and Analysis, Fukuoka 1   117 - 122 2015.12

    Research paper (conference, symposium, etc.), Single Work

display all >>

Page Top ▲

Papers, etc., Registered in KOARA 【 Display / hide 】

Page Top ▲

Presentations 【 Display / hide 】

  • 離散群上のランダム・ウォークと調和写像

    井関裕靖

    [Domestic presentation]  2025年度福岡大学幾何学研究集会, 

    2026.03
    , 

    Oral presentation (invited, special)

  • Harmonic maps and random walks on countable groups

    Hiroyasu Izeki

    Groups and Geomtry Seminar, University of Geneva, 

    2024.03
    , 

    Public lecture, seminar, tutorial, course, or other speech

  • 可算群上のランダム・ウォークと調和写像

    井関裕靖

    [Domestic presentation]  リーマン幾何と幾何解析, 

    2024.02
    , 

    Oral presentation (invited, special)

  • 可算群上のランダムウォークと調和写像

    井関裕靖

    [International presentation]  Frontiers of Riemannian Geometry ~Curvature, Convergence, Concentration~, In honor of the 60th birthday of Takashi Shioya, 

    2023.11
    -
    2023.12
    , 

    Oral presentation (invited, special)

  • Harmonic maps and random walks on countable groups

    Hiroyasu Izeki

    Geometry beyond Riemann: Curvature and Rigidity, 

    2023.10
    , 

    Oral presentation (invited, special)

display all >>

Page Top ▲

Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 同変境界写像を基盤とする幾何学的剛性理論の構築

    2025.04
    -
    2030.03

    MEXT, JSPS, Grant-in-Aid for Scientific Research, 基盤研究(B), Research grant, Principal investigator

  • Laplacian-eigenvalue maximization and minimal surface

    2022.04
    -
    2027.03

    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Coinvestigator(s)

  • 幾何学的剛性理論の深化

    2020.04
    -
    2025.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 井関 裕靖, Grant-in-Aid for Scientific Research (B), Research grant, Principal investigator

  • Rigidity of non-isometric actions of discrete groups and non-linear spectral gap

    2017.04
    -
    2022.03

    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Grant-in-Aid for Scientific Research (B), Research grant, Coinvestigator(s)

    　View Summary

    昨年度に引き続き, 球面S^n内の高種数の極小閉曲面を構成する問題について研究を行った. 研究の動機として, ラプラシアンの第1固有値を最大化する閉曲面上の計量が球面への極小はめこみによる誘導計量として与えられることが知られており, したがって, 球面内の高種数の極小閉曲面を構成することで, そのような最大化計量の候補が得られるということがある. 種数3以上の場合に最大化計量が未知であるので, とくに種数が低い例を与えることを目指している.
    LawsonによるS^3内の高種数極小閉曲面の構成を高次元化し, S^nの3角形分割として正2^{n+1}胞体を用いることで高種数の極小閉曲面を構成した. ただ, この構成で得られる極小閉曲面は自己交叉点を多く持ち, しかも種数が高くなる傾向がある(S^5, S^6で種数5, S^7で種数49等). 最大化計量を与える極小閉曲面は, 高い対称性を持つとともに, 自己交差が少ないことが期待されるので, 今後, 別の構成法を考案して, 自己交叉が少なく種数も低い例を見出したい.
    また, 昨年度に引き続き, 有限グラフのユークリッド空間への埋め込みに関する最適化問題と線形スペクトルギャップの最大化問題について研究を行なった. この研究は, 有限グラフの非線形スペクトルギャップの研究に動機付けられたものである. 類似の埋め込み最適化問題としてGoering-Wappler-Helmbergによるものが知られていたが, 両者の埋め込み最適化問題の関係を明らかにすることにより, 我々の埋め込み最適化問題の最適値と第線形スペクトルギャップの最大値の間にもある等式が成立することが示せた. また, アルキメデス多面体を始めとして対称性の高い様々な多面体について, Goering達および我々の埋め込み最適化問題の解を求めることができた.

  • An approach to the superrigidity of infinite discrete groups via random groups

    2013.04
    -
    2018.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, IZEKI Hiroyasu, NAYATANI Shin, KONDO Takefumi, Grant-in-Aid for Scientific Research (B), Principal investigator

    　View Summary

    The group is an algebraic object which also gives a description of symmetries of spaces. Some important and interesting groups often admits a property called "superrigidity", which we tried to understand as an extremal property among that involving infinite discrete groups. We could show that a fixed-point property, which should be considered to be an important aspect of superrigidity, is shared by finitely presented groups with overwhelming probability.

display all >>

Page Top ▲

Awards 【 Display / hide 】

  • 日本数学会建部賢弘賞

    IZEKI Hiroyasu, 1998.09, 日本数学会

    Type of Award： Award from Japanese society, conference, symposium, etc.

Page Top ▲
 

Courses Taught 【 Display / hide 】

  • DOCTORAL RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES

    2026

  • MATHEMATICS 2B

    2026

  • GRADUATE RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES 2

    2026

  • MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY A

    2026

  • MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY C

    2026

display all >>

Page Top ▲

Courses Previously Taught 【 Display / hide 】

  • INDEPENDENT STUDY FOR EXCHANGE STUDENT A

    Keio University

    2025.04
    -
    2026.03

  • MATHEMATICAL ANALYSIS 1

    Keio University

    2023.04
    -
    2024.03

  • MATHEMATICS 2B

    Keio University

    2022.04
    -
    2023.03

  • FOUNDATION FOR MATHEMATICAL SCIENCE 1 AND EXERCISE

    Keio University

    2022.04
    -
    2023.03

  • TOPICS IN GEOMETRY C

    Keio University

    2021.04
    -
    2022.03

display all >>

Page Top ▲
 

Memberships in Academic Societies 【 Display / hide 】

  • Mathematical Society of Japan, 

    1990.04
    -
    Present
Page Top ▲

Committee Experiences 【 Display / hide 】

  • 2025.07
    -
    2027.06

    日本数学会教育研究資金問題検討委員会委員長

  • 2024.07
    -
    Present

    Journal of Mathematical Society of Japan 編集委員

  • 2024.07
    -
    2028.06

    日本数学会教育研究資金問題検討委員会委員

  • 2021.04
    -
    2023.03

    日本数学会幾何学分科会評議員

  • 2020.04
    -
    2024.03

    日本数学会幾何学分科会幹事

display all >>

Page Top ▲