Program Overview

Introduction to the University Program

The Mathematics Graduate Major offers a wide variety of courses, allowing students to study advanced mathematical theories according to their interests. In addition to normal courses, intensive courses (known as Special Lectures) are also offered, enabling students to learn about topics that are currently the subject of intense research.

Master's Program

The Master's Program is a 2-year program that provides students with the opportunity to develop their mathematical theories, logical thinking, and critical observation skills. The program is divided into two main categories: Advanced Lectures and Special Lectures in algebra, geometry, and analysis.

Advanced Lectures

In the Advanced Lectures, students learn content that is generally considered a requirement for their field of study.

Special Lectures

In the Special Lectures, cutting-edge content that is currently the subject of active research is explained. Students also participate in Research Seminars and Special Mathematics Research, where they acquire knowledge by reading highly advanced technical texts and academic papers, and use that knowledge to tackle particular research questions.

Research Areas

The Master's Program covers a range of research areas, including:

• Algebra
  • Representation theory
  • Algebraic geometry
  • Arithmetic geometry
  • Number theory
  • Analytic number theory
  • Automorphic form theory
• Analysis
  • Partial differential equations
  • Global calculus of variations
  • Nonlinear analysis
  • Complex analysis
  • Probabilistic analysis
  • Dynamical systems theory
• Geometry
  • Fiber bundles
  • Differential topology
  • Knot theory
  • Low-dimensional manifold theory
  • Curved surfaces
  • Riemannian geometry
  • Global geometry
  • Hodge theory
  • Complex manifolds

Doctoral Program

The Doctoral Program is a 3-year program that provides students with the opportunity to perform full-fledged research based on the understanding of cutting-edge mathematics learned in the Master's Program. Students deepen their understanding of their specialized area and compose an academic paper of a standard that could be submitted to journals.

Research Areas

The Doctoral Program covers a range of research areas, including:

• Algebra
  • Representation theory of affine Hecke algebra and quantum groups
  • Algebraic and geometric structures related to Macdonald polynomials
  • Discrete Painlevé equations
  • Anabelian geometry
  • Witten zeta functions
• Analysis
  • The explosion problem of nonlinear heat equations
  • Introduction to random complex dynamics
  • Conformal mapping of Riemann surfaces
  • Introduction to geometric analysis
  • Introduction to the large deviation principle
  • Boundary value problems of elliptic equations
  • The Oka-Cartan theory
• Geometry
  • Rigidity problem in Riemannian geometry
  • Combinatorial group theory
  • Ricci flow
  • The Yamabe problem
  • Real singular point theory
  • Contact topology
  • Generalized Kähler structures

Completion and Advancement

Applicants must pass an advancement assessment to advance from a master's program to a doctoral program. Other universities' graduates and working adults must pass an entrance assessment to advance from another university to a doctoral program.