Department of Mathematics Laboratories

Algebra

Rubik’s Cube is intimately related to permutation groups

  • Analytic and algebraic study of the distribution of units of an algebraic number field
  • Study of non-commutative differential structures in reflection groups and integrable systems, as well as combinatorial commutative algebra
  • Study of algebraic invariants such as the adjacency matrix of a graph and spectra of a Laplacian matrix

Geometry

The above two surfaces have the same topology

  • Research on mathematical phenomena from a geometrical point of view
  • Variational problems in geometry
  • Transformation groups and moduli of congruence class of submanifolds
  • Knot theory

Analysis

The Mandelbrot set defined by iterative synthesis of a second-order polynomial

  • Study of harmonic functions as prototypes in many fields of mathematics
  • Study of fundamental solutions of partial differential equations derived from natural phenomena
  • Study of the singularities of solutions of partial differential equations

Note: Figure shows the Mandelbrot set defined by iterative synthesis of a second-order polynomial.
Complexity created from simple things, and simple beauty hidden in complexity. There is no end to the quests of analysis.


Mathematical Analysis of Information

The mandala, which is said to represent the mystery of the Universe, is related to the fractal known as the Sierpinski Carpet

  • Theory of infinite dimensional stochastic analysis and its applications
  • Study of the global structure of Markov processes from the viewpoint of fluctuations
  • Study of probability theory, in particular, ergodic theory and symbolic dynamical systems
  • Study related to mathematical finance

Computer Science

Tower of Hanoi created by students using Processing (JAVA programming)

  • Application of C language programming to number theory, numerical analysis, combinatorics, etc.
  • Study of mathematics and programming using Computer Algebra System (CAS)
  • MFC programming
  • JAVA programming