Tsuyoshi Kato

Tsuyoshi Kato

 

Name

Tsuyoshi Kato

 

Primary department

Org1 Org2 Org3 Job title
Graduate School of Science Mathematics and Mathematical Sciences   Professor

Research Topics

(1) Non compact geometric analysis
(2) Non commutative geometry
(3) Dynamical scale transform

 

Overview of your research

Atiyah-Singer index theorem is a monumental theory in differential topology. Later around 2000 year, it has created two main streams where one is non linear moduli theory in topology and the other is the index theorem on non compact spaces. My research objective in (1) (2) is to construct moduli theory over non compact spaces by unifying these two subjects. Tropical geometry is a kind of dynamical scale transform, which is also called ultra-discretization, and the objective in (3) is to apply such scale transform to geometric objects such as automata groups.

 

Fields of research (key words)

Non compact geometric analysis, Non commutative geometry, Dynamical Scale transform