In the word of mathematics, the symmetric structures on spaces are described by groups.
We call such symmetric space a space with group action.
My research interest lies in geometry and topology of the spaces with torus actions.
In this decades, the area so-called toric topology has been emerged.
Roughly speaking, toric topology can construct bridges among different areas (geometry, algebra and combinatorics) by the study of the spaces with torus actions.
In the near future, I would like to continue to study toric topology more deeply and challenge to solve open problems.