Toshihiko Masuda | Last modified date：2020.01.17 |

Graduate School

Undergraduate School

E-Mail

Academic Degree

Ph. D. (Mathematical Sciences)

Country of degree conferring institution (Overseas)

No

Field of Specialization

operator algebra

Total Priod of education and research career in the foreign country

00years00months

Outline Activities

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.

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.

Research

**Research Interests**

- Research of outer actions of discrete groups on factors

keyword : outer action

2010.01. - Research of one-parameter automorphism groups on factors

keyword : one-parameter automorphism groups

2010.01～2014.03. - Research of actions of compact groups on factors

keyword : factor, compact group, action

2005.04I study minimal actions of compact groups on factors with coauthor Dr. Tomatsu. We developed ultraproduct technique and proved the Rohlin type theorem and cohomology vanishing theorem. By intertwining argument, we classify outer coactions of compact groups on the injective factor of type II_1. Through duality theorem, we show the uniqueness of minimal actions. In type III case, it seems that we can classify actions by combining the above results and structure theorem of type III factors. So we are now studying along this idea.. - Group actions on subfactors

keyword : subfactor, group action

1997.04～2004.04I studied group actions on subfactors. I introduced cohomological invariants, and classified actions by these invariants under some nice conditions..

**Academic Activities**

**Papers**

Educational

**Educational Activities**

In 2010, I give the lecture of linear algebra for undergraduated students,

that of functional analysis for graduated students of mathematics,

and

that of Fourier analysis for students in the course of technology. In the

lecture of linear algebra, I first teach the solution of linear equations, computations of determinants.

Then I teach the theory of abstract linear algebra.

In the lecture of functional analysis, I taught general theory of Hibert spaces and spectral decomposition of compact

operators.

In the lecture of Fourier analysis, I teach the computations and applications to differential equations

that of functional analysis for graduated students of mathematics,

and

that of Fourier analysis for students in the course of technology. In the

lecture of linear algebra, I first teach the solution of linear equations, computations of determinants.

Then I teach the theory of abstract linear algebra.

In the lecture of functional analysis, I taught general theory of Hibert spaces and spectral decomposition of compact

operators.

In the lecture of Fourier analysis, I teach the computations and applications to differential equations

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