# Algebraic Topology Laboratory

# Understanding a high or infinite dimensional world using mathematical formulas

A high-dimensional world that goes beyond three or four dimensions or infinite ones appears not only in mathematics but also physics and engineering. In physics, elementary particles are regarded as strings instead of points. The whole string in three-dimensional space is infinite. We are conducting research on algebraic topology, which explores such a high-dimensional or infinite world using algebraic methods. Our research is expected to be applicable to the number theory, algebraic geometry and other mathematical fields as well as diverse engineering fields.

## This lab is for this SDG activity:

## STUDY FIELDS

- Mathematics

## FOR SOCIETY

Two-way interactions of topology with other fields are increasingly desired. It is expected that topology will go beyond its boundary and interact with the domains of computer science, engineering (such as sensor networks), mathematics (such as number theory and algebraic geometry) and other sciences.

## RESEARCH THEMES

- Research on cohomology, such as algebraic, gauge and loop groups
- Research on Morse theory
- Research on Hopf Map