|Graduate School of Science||Mathematics and Mathematical Sciences||Professor|
(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