| Toshihiko Masuda | Last modified date：2024.04.17 |
Graduate School
Undergraduate School
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Homepage
https://kyushu-u.elsevierpure.com/en/persons/toshihiko-masuda
Reseacher Profiling Tool Kyushu University Pure
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..
Reports
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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