MASUDA TOSHIHIKO
Organization
Faculty of Mathematics Division of Analysis 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
Professor
Contact information
Profile
My research field is the theory of operator algebras. In the theory of
operator algebras, we research subalgebras of bounded linear
operators on Hilbert spaces. There are two classes of operator algebras,
the class of C^*-algebras and that of von Neumann algebras. I mainly
study von Neumann algebras. My main interests are the theory of subfactors, and
automorphism groups and group actions on von Neumann
algebras. In subfactor theory, I analyze the construction introduced by
Longo and Rehren, and the structure of subfactors of type III_1. I
also study coactions of finite groups by using subfactor theory. Now I
try to apply this argument for study of actions of compact groups.
External link
Degree
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Ph. D. (Mathematical Sciences)
Research History
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1999年4月〜2004年3月 高知大学理学部数理情報学科助手
Research Interests・Research Keywords
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Research theme：Research of one-parameter automorphism groups on factors
Keyword：one-parameter automorphism groups
Research period： 2010.1 - 2014.3
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Research theme：Research of outer actions of discrete groups on factors
Keyword：outer action
Research period： 2010.1
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Research theme：Research of actions of compact groups on factors
Keyword：factor, compact group, action
Research period： 2005.4
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Research theme：Group actions on subfactors
Keyword：subfactor, group action
Research period： 1997.4 - 2004.4
Papers
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Toshihiko Masuda
Publications of the Research Institute for Mathematical Sciences 56 ( 2 ) 391 - 400 2020.1
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Classification of Roberts actions of strongly amenable C-*-tensor categories on the injective factor of type III1 Reviewed International journal
Toshihiko Masuda
INTERNATIONAL JOURNAL OF MATHEMATICS 28 ( 7 ) 2017.6
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Classification of actions of discrete Kac algebras on injective factors Reviewed International journal
Toshihiko Masuda, Reiji Tomatsu
Memoirs of American Mathematical Society 245 ( 1160 ) 2016.7
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Rohlin flows on von Neumann algebras Reviewed International journal
Toshihiko Masuda, Reiji Tomatsu
Memoirs of American Mathematical Society 244 ( 1153 ) 2016.6
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Unified approach to classification of actions of discrete amenable groups on injective factors Reviewed International journal
683 1 - 47 2013.10
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Classification of minimal actions of a compact Kac algebra with amenable dual Reviewed International journal
Toshihiko Masuda, Reiji Tomatsu
Commucations in Mathematical Physics 2007.9
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Classification of actions of discrete amenable groups on subfactors of type III_\lambda Reviewed International journal
Masuda, Toshihiko
Proceedings of American Mathematical Society 1999.7
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Classification of strongly free actions of discrete amenable actions on subfactors of type III_0 Invited Reviewed International journal
Masuda, Toshihiko
Pacific Journal of Mathematics 1999.1
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An analogue of Longo's canonical endomorphism in bimodule theory and its application to asymptotic inclusions Reviewed International journal
Masuda, Toshihiko
International Journal of Mathematics 1999.1
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Classification of outer actions of discrete amenable groupoids on injective factors Invited Reviewed International journal
Toshihiko Masuda
Journal of Mathematical Society of Japan 74 ( 3 ) 873 - 901 2022.7
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Toshihiko Masuda
Mathematica Scandinavica 121 ( 1 ) 101 - 110 2017.4
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Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III Reviewed International journal
Toshihiko Masuda and Reiji Tomatsu
Journal of Functional Analysis 258 2010.1
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Approximate innerness and central triviality of endomorphisms Reviewed International journal
Toshihiko Masuda, Reiji Tomatsu
Advance in Mathematics 2009.1
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Classification of actions of duals of finite groups on the AFD factor of type II_1 Reviewed International journal
Toshihiko Masuda
Journal of Operator theory 2008.10
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Evans-Kishimoto type argument for actions of discrete amenable groups on McDuff factors Reviewed International journal
Toshihiko Masuda
Mathematica Scandianvica 2007.10
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An analogue of Connes-Haagerup approach for classification of subfactors of type III_1 Reviewed International journal
Toshihiko Masuda
Journal of Mathematical Society of Japan 57 ( 4 ) 959 - 1001 2005.1
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Classification of approximately inner actions of discrete amenable groups on strongly amenable subfactors Reviewed International journal
Toshihiko Masuda
International Journal of Mathematics 16 ( 10 ) 1193 - 1206 2005.1
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Notes on group actions on subfactors Reviewed International journal
MASUDA, Toshihiko
Journal of Mathematical Society of Japan 2003.1
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On non-strongly free automorphisms of subfactors of type III_0 Reviewed International journal
MASUDA, Toshihiko
Canadian Mathematical Bulletin 2003.1
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Extension of automorphisms of a subfactor to the symmetric enveloping algebra Reviewed International journal
MASUDA, Toshihiko
International Journal of Mathematics 2001.1
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Generalization of Longo-Rehren construction to subfactors of infinite depth and amenability of fusion algebras Reviewed International journal
MASUDA, Toshihiko
Journal of Funcitional Analysis 2000.1
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Classification of outer actions of discrete amenable groupoids on injective factors Reviewed International journal
Toshihiko Masuda
Journal of Mathematical Society of Japan 1900
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Actions of discrete amenable groups into the normalizers of full groups of ergodic transformations Reviewed
Toshihiko Masuda
Ergodic theory and Dynamical Systems 1900
Presentations
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フォンノイマン環へのロホリン的流れ入門
増田俊彦
RIMS共同研究「作用素環論と種々の対称性」 2024.1
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エルゴード変換の充足群の正規化群への離散従順群の作用
増田俊彦
日本数学会秋季総合分科会函数解析分科会 2023.9
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III型因子環への離散カッツ環のモジュラー作用
増田 俊彦
研究集会「作用素環論の最近の進展」 2023.9
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Actions of discrete amenable groups into the normalizer of full groups of ergodic tranformations
2023.1
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Outer actions (G-kernels) of discrete amenable groupoids on injective factors,
2021.9
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Outer actions (G-kernels) of discrete amenable groupoids on injective factors,
2021.9
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Outer actions (G-kernels) of discrete amenable groupoids on injective factors,
2020.6
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On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III1
2019.12
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On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III1
2019.9
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Tannaka-Krein-Woronowicz duality from the viewpoint of Q-systems
2018.3
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冨田竹崎理論の紹介とそれに関連する話題
増田俊彦
第56回実函数論函数解析合同シンポジウム 2017.8
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強従順なC^*テンソル圏のロバーツ作用の分類について
増田俊彦
日本数学会 2018.5
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離散従順群の単射的因子環への外部的作用（G-kernel）の分類について
増田 俊彦
日本数学会 2016.9
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Connes の単射的III$_1$型因子環の分類についての議論の紹介と補足 (モジュラー 自己同型の近似的内部性について),
増田俊彦
作用素環の分類理論とその周辺 2015.2
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Braided system上のgradingとLongo-Rehren inclusion
増田俊彦
作用素環とその周辺分野の発展 2014.1
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Orbifold構成法での障害が消えるための十分条件
増田俊彦
日本数学会 2013.9
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フォンノイマン環上のロホリン的な流れの分類について
増田 俊彦
第５２回実函数論・函数解析学合同シンポジウム 2013.9
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Classification of group actions on von Neumann algebras
2013.5
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Rohlin flows on injective factors Invited International conference
Toshihiko Masuda
Conference on von Neumann Algebras and Related Topics 2012.1
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Rohlin flows on injective factors
2011.11
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フォンノイマン環への群・量子群作用の分類
増田俊彦
作用素環論とその関連分野の研究 2011.1
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離散従順群の単射的因子環へのモデル作用の構成について
増田俊彦
日本数学会 2010.9
-
Evans-岸本型のintertwining argumentの一般化と離散従順群の単射的因子環への作用の分類
増田俊彦
日本数学会 2009.9
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Evans-Kishimoto intertwining argumentの一般化による単射的因子環への離散従順群の作用の分類
増田俊彦
作用素環論とその関連分野の研究 2009.9
-
III$_0$ subfactorのnon-strongly free automorphismについて Invited
研究集会「作用素環論の多様性」 2001.1
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On non-strongly free automorphisms for subfactor of type III$_0$ Invited International conference
T.Masuda
Universita di Roma, seminar 2001.9
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On Longo-Rehren inclusions and Popa's symmetric enveloping algebras Invited International conference
.T.Masuda
mini-workshop ``Index Theorems and Modularity in Operator 2002.6
-
III$_1$型部分因子環におけるrelative bicentralizerについて Invited
増田 俊彦
「作用素論・作用素環論」研究集会 2002.10
-
因子環の自己同型にまつわる話題 Invited
増田 俊彦
第43回実函数論・函数解析学合同シンポジウム 2004.7
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On classification of minimal actions of a compact Kac algebra with amenable dual, (joint work with (R. Tomatsu.) Invited International conference
Toshihiko Masuda
US-Japan seminar 2007.1
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エルゴード変換の充足群の正規化群への離散従順群の作用
増田俊彦
京都作用素環セミナー 2023.6
MISC
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Tomita-Takesaki theory and its application to the structure theory of factors of type III Reviewed
Masuda Toshihiko
Mathematical Journal of Okayama University 2018.1
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Actions of groups and quantum groups on amenable factors
Toshihiko Masuda, Reiji Tomatsu
Sugaku exposition 2017.6
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従順因子環への群・量子群作用について Reviewed
戸松 玲治, 増田 俊彦
數學 2012.1
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単射的${ m III_1}$型因子環の一意性に関する覚書 (作用素環論における最近の分類問題について)
増田 俊彦
数理解析研究所講究録 2005.5
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$III_1$型部分因子環の分類について (作用素環における量子解析の展開)
増田 俊彦
数理解析研究所講究録 2004.1
-
M. Takesaki著"Theory of Operator algebras, II, III"
増田俊彦
数学 2003.10
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$III_0$ subfactorのnon-strongly free automorphismについて (作用素環論の多様性)
増田 俊彦
数理解析研究所講究録 2001.10
-
On classification of approximately inner actions of discrete amenable groups on strongly amenble subfactors (作用表環論の進展)
増田 俊彦
数理解析研究所講究録 2000.2
-
Extension of automorphisms of a subfactor to the symmetric enveloping algebra (Hilbert $C^*$-modules and groupoid $C^*$-algebras)
1999.8
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Asymptotic inclusion と Longo-Rehren の構成について(作用素環論における最近の発展)
増田 俊彦
数理解析研究所講究録 1997.2
-
An analogue of Longo's canonical endomorphism for bimodule theory and its application to the asymptotic inclusion
1996.8
Professional Memberships
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日本数学会
Committee Memberships
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日本数学会 函数解析分科会委員 Domestic
2020.3 - 2022.3
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Councilor Domestic
2015.3 - 2016.2
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日本数学会 地方区代議員 Domestic
2015.3 - 2016.2
Academic Activities
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世話人 International contribution
（ 東京大学 ） 2023.7
-
Screening of academic papers
Role(s)： Peer review
2022
-
世話人
作用素論作用素環論研究集会 （ 九州大学数理学研究院IMIオーディトリアム(zoomも使用したハイブリッド形式) ） 2021.11
-
世話人
作用素論作用素環論研究集会 （ オンライン形式 ） 2020.11
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Screening of academic papers
Role(s)： Peer review
2019
-
Screening of academic papers
Role(s)： Peer review
2018
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数学
2014.9 - 2018.6
Research Projects
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作用素環とその対称性についての研究
Grant number：22K03341 2022 - 2025
日本学術振興会 科学研究費助成事業 基盤研究(C)
Authorship：Principal investigator Grant type：Scientific research funding
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作用素環における自己同型からくる対称性の研究
Grant number：16K05180 2016 - 2022
日本学術振興会 科学研究費助成事業 基盤研究(C)
Authorship：Principal investigator Grant type：Scientific research funding
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作用素環論における自己同型群及び群作用の研究
Grant number：19740088 2007 - 2010
科学研究費助成事業 若手研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
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作用素環論における部分因子環の構造に関する研究
Grant number：14740119 2002 - 2004
科学研究費助成事業 若手研究(B)
Authorship：Principal investigator Grant type：Scientific research funding
Class subject
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数理科学特別講義Ⅷ
2023.10 - 2024.3 Second semester
-
線形代数学Ⅱ
2023.10 - 2024.3 Second semester
-
数理科学特論８
2023.10 - 2024.3 Second semester
-
関数解析大意
2023.4 - 2023.9 First semester
-
線形代数学Ⅰ
2023.4 - 2023.9 First semester
-
数学特論９
2023.4 - 2023.9 First semester
-
数学概論Ⅰ・演習
2023.4 - 2023.9 First semester
-
入門微分積分Ⅱ
2022.12 - 2023.2 Winter quarter
-
微分積分学Ⅱ
2022.10 - 2023.3 Second semester
-
入門微分積分Ⅰ
2022.10 - 2022.12 Fall quarter
-
微分積分学Ⅰ
2022.4 - 2022.9 First semester
-
数学概論Ⅰ・演習
2022.4 - 2022.9 First semester
-
作用素環論基礎・演習
2021.10 - 2022.3 Second semester
-
微分積分学Ⅱ
2021.10 - 2022.3 Second semester
-
微分積分学Ⅱ
2021.10 - 2022.3 Second semester
-
微分積分学Ⅰ
2021.4 - 2021.9 First semester
-
微分積分学Ⅰ
2021.4 - 2021.9 First semester
-
微分積分学
2020.10 - 2021.3 Second 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
-
微分積分学・同演習Ⅱ
2019.10 - 2020.3 Second semester
-
微分積分学・同演習Ⅱ
2019.10 - 2020.3 Second semester
-
解析学Ⅲ
2019.10 - 2020.3 Second semester
-
関数解析
2019.10 - 2020.3 Second semester
-
関数解析の基礎
2019.10 - 2020.3 Second semester
-
数理科学特別講義Ⅴ
2019.4 - 2019.9 First semester
-
微分積分学・同演習Ⅰ
2019.4 - 2019.9 First semester
-
微分積分学・同演習Ⅰ
2019.4 - 2019.9 First semester
-
数理科学特論５
2019.4 - 2019.9 First semester
-
数学概論Ⅰ・演習
2019.4 - 2019.9 First semester
-
関数解析の基礎
2018.10 - 2019.3 Second semester
-
解析学Ⅲ
2018.10 - 2019.3 Second semester
-
微分積分学・同演習Ｂ
2018.10 - 2019.3 Second semester
-
関数解析の基礎
2018.10 - 2019.3 Second semester
-
関数解析
2018.10 - 2019.3 Second semester
-
数学概論Ⅰ・演習
2018.4 - 2018.9 First semester
-
微分積分学・同演習Ａ
2018.4 - 2018.9 First semester
-
微分積分学・同演習Ⅲ
2018.4 - 2018.9 First semester
-
MMA講究C
2018.4 - 2018.9 First semester
-
微分積分学･同演習Ⅲ
2017.12 - 2018.2 Winter quarter
-
解析学Ⅲ
2017.10 - 2018.3 Second semester
-
微分積分学･同演習Ⅱ
2017.10 - 2017.12 Fall quarter
-
微分積分学･同演習Ⅰ
2017.4 - 2017.9 First semester
-
MMA講究C
2017.4 - 2017.9 First semester
-
線形代数学同演習B
2016.10 - 2017.3 Second semester
-
微分積分学同演習B
2016.10 - 2017.3 Second semester
-
関数解析
2016.4 - 2016.9 First semester
-
微分積分学同演習A
2016.4 - 2016.9 First semester
-
微分積分学
2016.4 - 2016.9 First semester
-
線形代数学同演習A
2016.4 - 2016.9 First semester
-
線形代数学同演習B
2015.10 - 2016.3 Second semester
-
微分積分学同演習B
2015.10 - 2016.3 Second semester
-
線形代数学同演習A
2015.4 - 2015.9 First semester
-
数学概論II
2015.4 - 2015.9 First semester
-
微分積分学同演習A
2015.4 - 2015.9 First semester
-
線形代数学同演習B
2014.10 - 2015.3 Second semester
-
微分積分学同演習II
2014.10 - 2015.3 Second semester
-
作用素環基礎演習
2014.4 - 2014.9 First semester
-
微分積分学同演習I
2014.4 - 2014.9 First semester
-
線形代数学同演習A
2014.4 - 2014.9 First semester
-
数学展望
2014.4 - 2014.9 First semester
-
線形代数学同演習B
2013.10 - 2014.3 Second semester
-
数学IIA
2013.10 - 2014.3 Second semester
-
線形代数学同演習A
2013.4 - 2013.9 First semester
-
解析学I
2013.4 - 2013.9 First semester
-
微分積分学同演習B
2012.10 - 2013.3 Second semester
-
数学IIA
2012.10 - 2013.3 Second semester
-
数学基礎演習III
2012.4 - 2012.9 First semester
-
解析学I
2012.4 - 2012.9 First semester
-
微分積分学同演習A
2012.4 - 2012.9 First semester
-
微分積分学同演習B
2011.10 - 2012.3 Second semester
-
数学IIA
2011.10 - 2012.3 Second semester
-
微分積分学同演習A
2011.4 - 2011.9 First semester
-
作用素環論大意
2011.4 - 2011.9 First semester
-
数学IIA
2010.10 - 2011.3 Second semester
-
線形代数学同演習B
2010.10 - 2011.3 Second semester
-
作用素環論大意
2010.4 - 2010.9 First semester
-
線形代数学同演習A
2010.4 - 2010.9 First semester
-
線形代数学同演習B
2009.10 - 2010.3 Second semester
-
微分積分学同演習B
2009.10 - 2010.3 Second semester
-
数学IIA
2009.10 - 2010.3 Second semester
-
微分積分学同演習A
2009.4 - 2009.9 First semester
-
線形代数学同演習A
2009.4 - 2009.9 First semester
-
線形代数同演習B
2008.10 - 2009.3 Second semester
-
微分積分学同演習B
2008.10 - 2009.3 Second semester
-
数学IIA
2008.10 - 2009.3 Second semester
-
線形代数同演習A
2008.4 - 2008.9 First semester
-
数学IA
2007.4 - 2007.9 First semester
-
微分積分学同演習A
2007.4 - 2007.9 First semester
-
作用素環論基礎・演習
2006.10 - 2007.3 Second semester
-
微分積分学・同演習B
2006.10 - 2007.3 Second semester
-
基礎数学演習III
2006.4 - 2006.9 First semester
-
微分積分学・同演習A
2006.4 - 2006.9 First semester
-
作用素環論基礎・演習
2005.4 - 2005.9 First semester
-
数学基礎演習Ⅲ
2005.4 - 2005.9 First semester
-
微分積分A
2004.4 - 2004.9 First semester
-
微分積分続論
2004.4 - 2004.9 First semester
Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.
-
2012 東京大学数理科学研究院 Classification:Intensive course Domestic/International Classification:Japan
Semester, Day Time or Duration：7/4-7/8
Social Activities
-
2023年5月21日に開催された入試連絡会において九州内の高校教員を対象とした講演を行った。
2023
-
鹿児島県の教員を対象とした、令和５年度教材研究会において講演を行った。
2023
-
公開講座「現代数学入門」の世話人、及び講師
九州大学数理学研究院、マスフォアインダストリ研究所 九州大学伊都キャンパスウェスト1号館IMIオーディトリアム 2014.7
Travel Abroad
-
2008.11
Staying countory name 1：Austria Staying institution name 1：シュレーディンガー研究所
-
2007.10 - 2007.12
Staying countory name 1：Canada Staying institution name 1：フィールズ研究所