Updated on 2024/07/28

Information

 

写真a

 
SATO YASUHIKO
 
Organization
Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics（Joint Appointment）
Graduate School of Mathematics Department of Mathematics（Joint Appointment）
Joint Graduate School of Mathematics for Innovation （Joint Appointment）
Title
Associate Professor
External link

Research Interests・Research Keywords

  • Research theme：The main theme of my research is the theory of operator algebras and their group actions. Although operator algebras are basically represented on infinite dimensional linear spaces, it is important to consider approximations by finite dimensional spaces in several topologies. Often times, an elementary technique of finite dimensional matrices plays a key role. The main goal of my research is to characterize classifiable C*-algebras abstractly. In particular, I am interested in the following problems. 1. Amenable C*-algebras, nuclear dimension, and Toms-Winter conjecture, 2. The classification theory of group actions on the Jiang-Su algebra, 3. Quasidiagonality, Rosenberg conjecture, and Blackadar-Kirchberg conjecture.

    Keyword：Operator Algebras, C*-algebras, Group Actions, Nuclear Dimension, Classification Theory

    Research period： 2020.4 - 2023.4

Awards

  • 作用素環賞

    2020.11   作用素環後援会  

    　More details

    https://www.mathsoc.jp/assets/file/publications/tushin/2504/6-OperatorRing.pdf

  • 建部賢弘賞奨励賞

    2012.9   日本数学会  

Papers

  • Rationally AF algebras and KMS states of Z-absorbing C*-algebras Invited International journal

    G.A.Elliott, Y. Sato

    arXiv:2207.11653   2022.9

    　More details

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

    Repository Public URL： https://hdl.handle.net/2324/7173589

  • On the Bundle of KMS State Spaces for Flows on a Z-Absorbing C*-Algebra Reviewed International journal

    Communications in Mathematical Physics (2022)   2022.5

    　More details

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

  • Endomorphisms of Z-absorbing C*-algebras without conditional expectations Reviewed International journal

    Yasuhiko Sato

    Munster Journal of Mathematics   2023.9

    　More details

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

  • On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra International journal

    Yasuhiko Sato, G. E. Elliott, K. Thomsen

    https://arxiv.org/search/?query=Thomsen+Sato&searchtype=all   2021.12

    　More details

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

  • 2-positive almost order zero maps and decomposition rank Reviewed International journal

    Yasuhiko Sato

    Journal of Operator Theory   2020.12

    　More details

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

  • Covering dimension of C∗-algebras and 2-coloured classification Reviewed

    257 ( 1233 )   1 - 112   2019.1

    　More details

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

    We introduce the concept of finitely coloured equivalence for unital ∗-homomorphisms between C∗-algebras, for which unitary equivalence is the 1- coloured case. We use this notion to classify ∗-homomorphisms from separable, unital, nuclear C∗-algebras into ultrapowers of simple, unital, nuclear, Z-stable C∗- algebras with compact extremal trace space up to 2-coloured equivalence by their behaviour on traces; this is based on a 1-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application we calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, Z-stable C∗-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, we derive a "homotopy equivalence implies isomorphism" result for large classes of C∗-algebras with finite nuclear dimension.

    DOI： 10.10.1090/memo/1233

  • Actions of amenable groups and crossed products of Z-absorbing C*-algebras Reviewed

    Yasuhiko Sato

    Advanced Studies in Pure mathematics   80 ( 5 )   189 - 210   2019

    　More details

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

  • C*環の分類理論の進展 Reviewed

    佐藤 康彦

    数学   70 ( 1 )   44 - 62   2018

    　More details

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

    DOI： 10.11429/sugaku.0701044

  • Nuclear dimension and Z -stability Reviewed

    Yasuhiko Sato, Stuart White, Wilhelm Winter

    Inventiones Mathematicae   202 ( 2 )   893 - 921   2015.11

    　More details

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

    DOI： 10.1007/s00222-015-0580-1

  • Elementary amenable groups are quasidiagonal Reviewed

    Geometric and Functional Analysis   25 ( 1 )   307 - 316   2015.1

    　More details

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

    DOI： 10.1007/s00039-015-0315-x

  • Ƶ-stability of crossed products by strongly outer actions II Reviewed

    136 ( 6 )   1441 - 1496   2014.12

    　More details

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

    We consider a crossed product of a unital simple separable nuclear stably finite Ƶ-stable C∗-algebra A by a strongly outer cocycle action of a discrete countable amenable group Γ. Under the assumption that A has finitely many extremal tracial states and Γ is elementary amenable, we show that the twisted crossed product C∗-algebra is Ƶ-stable. As an application, we also prove that all strongly outer cocycle actions of the Klein bottle group on Ƶ are cocycle conjugate to each other. This is the first classification result for actions of non-abelian infinite groups on stably finite C∗-algebras.

    DOI： 10.1353/ajm.2014.0043

  • Decomposition rank of UHF-absorbing c* -algebras Reviewed

    Hiroki Matui, Yasuhiko Sato

    Duke Mathematical Journal   163 ( 14 )   2687 - 2708   2014.1

    　More details

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

    DOI： 10.1215/00127094-2826908

  • Strict comparison and Z-absorption of nuclear C *-algebras Reviewed

    Hiroki Matui, Yasuhiko Sato

    Acta Mathematica   209 ( 1 )   179 - 196   2012.10

    　More details

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

    DOI： 10.1007/s11511-012-0084-4

  • Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary

    Yasuhiko Sato

    arXiv:1209.3000   2012.10

    　More details

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

  • Z-Stability of Crossed Products by Strongly Outer Actions Reviewed

    Hiroki Matui, Yasuhiko Sato

    Communications in Mathematical Physics   314 ( 1 )   193 - 228   2012.7

    　More details

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

    DOI： 10.1007/s00220-011-1392-9

  • Discrete amenable group actions on von Neumann algebras and invariant nuclear C*-subalgebras

    Yasuhiko Sato

    arXiv:1104.4339   2011.10

    　More details

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

  • The Rohlin property for automorphisms of the Jiang-Su algebra Reviewed

    Yasuhiko Sato

    Journal of Functional Analysis   259 ( 2 )   453 - 476   2010.7

    　More details

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

    DOI： 10.1016/j.jfa.2010.04.006

  • Certain aperiodic automorphisms of unital simple projectionless C* -algebras Reviewed

    Yasuhiko Sato

    International Journal of Mathematics   20 ( 10 )   1233 - 1261   2009.10

    　More details

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

    DOI： 10.1142/S0129167X09005741

  • A generalization of the Jiang-Su construction

    Yasuhiko Sato

    arXiv:0903.5286   2009.7

    　More details

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

▼display all

Professional Memberships

  • 日本数学会

Academic Activities

  • 主催者

    RIMS共同研究プログラム 「作用素環論における群作用と数理物理の関連」  （ 京都大学　RIMS ） 2023.1

    　More details

    Type：Competition, symposium, etc. 

    Number of participants：50

Research Projects

  • 作用素環における条件付き期待値と分類戦略の応用

    Grant number：24K06762  2024 - 2028

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    　 More details

    Authorship：Principal investigator  Grant type：Scientific research funding

  • 作用素環の核型次元の研究

    2020.6

  • 作用素環の核型次元の研究

    2019 - 2022

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    　 More details

    Grant type：Scientific research funding

  • 作用素環の分類理論と群や力学系への応用

    2015 - 2019

    科学研究費助成事業  若手研究(B)

    　 More details

    Grant type：Scientific research funding

  • Jiang-Su 環の群作用の分類とその応用

    2013 - 2015

    日本学術振興会  科学研究費助成事業  研究活動スタート支援

    　 More details

    Grant type：Scientific research funding

  • 作用素環の自己同型と実数群作用の分類

    2011 - 2012

    科学研究費助成事業  若手研究(B)

    　 More details

    Grant type：Scientific research funding

▼display all

Class subject

  • 解析学Ⅲ

    2024.10 - 2025.3   Second semester

  • 数理科学特別講義XⅢ

    2024.10 - 2025.3   Second semester

  • 数理科学特論１３

    2024.10 - 2025.3   Second semester

  • 数学特論９

    2024.4 - 2024.9   First semester

  • 関数解析大意

    2024.4 - 2024.9   First semester

  • 解析学Ⅲ

    2023.10 - 2024.3   Second semester

  • 関数解析の基礎

    2023.10 - 2024.3   Second semester

  • 線形代数学Ⅱ

    2023.10 - 2024.3   Second semester

  • 微分積分学Ⅱ

    2023.10 - 2024.3   Second semester

  • 線形代数学Ⅰ

    2023.4 - 2023.9   First semester

  • 微分積分学Ⅰ

    2023.4 - 2023.9   First semester

  • 微分積分学Ⅱ

    2022.10 - 2023.3   Second semester

  • 線形代数学Ⅱ

    2022.10 - 2023.3   Second semester

  • コアセミナーⅡ

    2022.10 - 2023.3   Second semester

  • 関数解析大意

    2022.4 - 2022.9   First semester

  • 線形代数学Ⅰ

    2022.4 - 2022.9   First semester

  • 数学特論９（関数解析）

    2022.4 - 2022.9   First semester

  • 微分積分学Ⅰ

    2022.4 - 2022.9   First semester

  • 数理科学特別講義XⅣ

    2021.10 - 2022.3   Second semester

  • 微分積分学Ⅱ

    2021.10 - 2022.3   Second semester

  • コアセミナーⅡ

    2021.10 - 2022.3   Second semester

  • 数理科学特論１４

    2021.10 - 2022.3   Second semester

  • 微分積分学Ⅰ

    2021.4 - 2021.9   First semester

  • 数学特論９（関数解析）

    2021.4 - 2021.9   First semester

  • 関数解析大意

    2021.4 - 2021.9   First semester

  • 線形代数学・同演習Ｂ

    2020.10 - 2021.3   Second semester

  • 微分積分学・同演習Ｂ

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習Ａ

    2020.4 - 2020.9   First semester

  • 微分積分学・同演習Ⅲ

    2020.4 - 2020.9   First semester

  • 微分積分学・同演習Ａ

    2020.4 - 2020.9   First semester

▼display all

FD Participation

  • 2021.7   Role：Participation   Title：数理学府FD

    Organizer：[Undergraduate school/graduate school/graduate faculty]

  • 2021.3   Role：Participation   Title：数理学府FD

    Organizer：[Undergraduate school/graduate school/graduate faculty]

Travel Abroad

  • 2015.4 - 2017.3

    Staying countory name 1：United States   Staying institution name 1：パーデュー 大学

    Staying countory name 2：Denmark  

    Staying countory name 3：United States  

  • 2013.4 - 2013.11

    Staying countory name 1：Denmark   Staying institution name 1：コペンハーゲン 大学

    Staying countory name 2：Denmark  

    Staying countory name 3：United States  

  • 2012.4 - 2012.10

    Staying countory name 1：United States   Staying institution name 1：オレゴン 大学

    Staying countory name 2：Denmark  

    Staying countory name 3：United States