My research concerns topology of Lie groups and related spaces. More specifically, I study compact Lie groups, their homogeneous spaces, and manifolds with Lie group actions through topological invariants such as the (equivariant) cohomology. My recent research has focussed on the torus equivariant topology of flag manifolds and toric manifolds. My main technical tools are the classical methods of algebraic topology, such as spectral sequences, cohomology operations, and rational homotopy theory.
My research is partially supported by JSPS/KAKENHI, Grant-in-Aid for Scientific Research (C) 18K03304.
In a different direction, I pursue a research programme on applications of topology in computer sciences, in particular, computer graphics, data analysis, and information security.
This part of my research is supported by JST/PRESTO.