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Science of Environment and Mathematical Modeling

Research on Topology of Gauge Groups

What is a big difference between the left and right figures?

The two figures differ, of course, in the number of holes. In this way, one branch of geometry that links a space (figure) to an algebraic object (e.g., a number) to examine the rough properties of the space by using the algebraic object is called algebraic topology. The concept of algebraic topology is very natural and intuitive. The technique is thus used widely, not only in geometry but also in other areas of mathematics, such as algebra and combinatorics. Algebraic topology has recently expanded its applications, ranging from sensor networks or robotics and structural analysis of proteins to big data analytics. Algebraic topology is an extremely free mathematics. I study this algebraic topology.

The two figures differ, of course, in the number of holes. In this way, one branch of geometry that links a space (figure) to an algebraic object (e.g., a number) to examine the rough properties of the space by using the algebraic object is called algebraic topology. The concept of algebraic topology is very natural and intuitive. The technique is thus used widely, not only in geometry but also in other areas of mathematics, such as algebra and combinatorics. Algebraic topology has recently expanded its applications, ranging from sensor networks or robotics and structural analysis of proteins to big data analytics. Algebraic topology is an extremely free mathematics. I study this algebraic topology.

- Topology of Lie Groups
- Homotopy type theory
- Generalized Cohomology

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