Research Fields of the Department of Mathematics

The integers used since the dawn of humanity lead to advanced mathematics through the study of algebraic structures that transcend basic arithmetic operations. New theories, like Iwasawa theory, are still being created today. Applying number theory, it can be shown that among pairs of right triangles and isosceles triangles with integer side lengths, the only ones (excluding similar triangles) that have equal perimeters and areas are those shown in the figure above. This is also deeply connected to cryptography and coding theory, which form the foundation of the information society.

Geometry is the study of representing the characteristics of figures with numbers and investigating their properties. For example, the characteristics of plane figures are represented by quantities such as lengths, angles, and areas. In this department, we study more complex figures, including knots (mathematical abstractions of tangled threads), the “invariants” that describe their entanglement, as well as “curvature” that represents the degree of bending in curved surfaces like spheres.

By changing the scale at which we view things, we can analyze various natural, social, and economic phenomena in greater detail. For example, the diffusion equations that describe the diffusion of ink or heat on a macroscopic scale can be derived as the accumulation of the random motion of individual ink particles or atoms. In this department, research is being carried out on probability theory and partial differential equations, which play an important role in these types of problems.

Statistics serves as a methodology for understanding various phenomena occurring around us, such as stock price movements and factors contributing to epidemics. In statistical science, we begin with fundamental statistical procedures such as data summarization and visualization, then harness mathematical models to obtain deep insights into phenomena and to support decision-making. To that end, the course systematically covers everything from data collection and modeling to estimation algorithms, analysis of statistical behavior, and interpretation of results.