Our department conducts applied research from a geometrical standpoint, using modern advances in geometry (differential geometry and topology) as a base.
As for the relationship between topology and physics, we intend to explain how supersymmetric gauge theory has a structure in common with three-dimensional manifold theory and knot theory. In our study of quantum walks, we will develop our research from the standpoint of discrete geometric analysis and aim to provide feedback to computer science.
We promote collaboration between mathematics and other scientific fields by focusing on pattern dynamics that appear in natural phenomena and analyzing them mathematically. For example, we work on the pattern dynamics of reaction-diffusion systems and their applications to material science, as well as the pattern dynamics of flow fields.
The Division of Mathematical Analyses on Life and Social Sciences studies various mathematical models related to life science, medicine, finance, insurance, and service industries. Our research includes numerical simulations based on mathematical models to understand the dynamics of blood flow, as well as research to explore the mathematical structure and stability of the nervous system and chemotaxis mathematical models that explain the behavior of white blood cells.
We also conduct research aimed at solving problems in service industries based on recent research in data science including Bayesian statistics, as well as research on mathematical models of the economy, including analysis of asset prices and quantitative risk management in financial markets.
In the Department of Discrete Structure Analysis, we mostly work on the mathematical analysis of combinational structures and their application. Specifically, we work on the paradigm of building an analysis for discrete structures with the utilization of big data at the forefront of our research. We work to contribute to the reliability of communications by creating a new theory of algebraic coding through our work on quantum codes and DNA codes.