# Representation Theory Laboratory

# Thinking from the perspective of symmetry

Representation theory studies how symmetry is expressed in (vector) spaces. For example, the space of functions on a sphere exhibits a symmetry under rotating the sphere and then applying a function. Through such symmetries, problems related to the original space can sometimes be reduced to simpler problems (such as separation of variables when solving partial differential equations). In our research laboratory, we aim to study the structure of spaces with symmetry and work towards concrete problem-solving.

## This lab is for this SDG activity:

## STUDY FIELDS

- Mathematics

## FOR SOCIETY

By studying mathematics, one can develop the ability to understand complex logic rigorously, comprehend what is essential in things, and explain them in a way that is understandable to others. This can become a source for developing society.

## RESEARCH THEMES

- Lie theory
- Representation theory of Lie groups