21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

Research Areas at the Department of Mathematics

Mathematics is often described as the foundation of various scientific studies. Because of its traditional and fundamental nature familiar to us, mathematical study is usually considered as an academic discipline based on the past achievements. Indeed, mathematics does have a long rich history. At the same time, however, it continues to grow rapidly. A number of academic journals are published and revamped every year, and research conferences and seminars are regularly held to bring together researchers from all around the world.

With rapid advancements witnessed in various fields of science, the scientific community is always pursuing new types of mathematics. Breakthroughs in mathematics, on the other hand, are also contributing to new perspectives on other scientific disciplines. Many new fields of mathematics have been born from attempts to solve particular phenomena by formalizing them with mathematical expressions. This dynamics is exemplified in the relationship between the evolution of Modern Physics and the emergence of new mathematical approaches, such as Functional Analysis, Differential Geometry, Differential Equations, Topology, Algebraic Geometry, Algebraic Analysis, Probability Theory, and Dynamical Systems. In their early forms, such new approaches are largely unsophisticated; however, the very efforts to seek greater sophistication and define essential elements through formalization have led to the overall progress in mathematics.

The Department of Mathematics at Hokkaido University preserves this spirit, covering a wide range of research areas --- from theory-driven approaches that mainly seek to achieve theoretical sophistication, such as Number Theory, to more practical approaches that employ computers for calculations of various phenomena. Our diverse curriculum also includes what is known as Mathematical Sciences.

21st Century COE Program : Mathematics of Nonlinear Structure via Singularity