Motoko KOTANI【小谷 元子】, Professor

Research Field

 My research field is Geometry, studying symmetries of figures. Symmetry is described by Group in Mathematics. Geometry in the 20th century has been developed mainly in connection with group theory. Understanding of a discrete group has been accelerated by introducing geometric structures into it, although it had remained almost untouched until recently, due to lack of appropriate tools. I studied random walks to investigate discrete groups, which raised my interest in the interplay of Geometry and Probability Theory. Probability Theory provides a useful tool to understand random and complex phenomena in the physical world. I now work to establish a mathematical theory by using Discrete Geometric Analysis to clarify how macroscopic dynamics, such as an electric current or a heat flow in materials, are controlled by their microscopic geometric structures.


 When I was a university student, the forefront of mathematical research looked far out of my reach. I was almost crushed by a sad and hopeless feeling, accepting the fact that I was not able to participate in the creation of a beautiful, attractive world of mathematics that only geniuses were allowed to do. However, I was wrong. I felt relieved when I found that mathematics is full of richness, and accepts all varieties of ideas, offering me complete freedom to pursue my own interests, driven by curiosity. If you encounter a world you devote yourself to work for, I truly believe that you will be welcomed to join there.


Personal Web Page Research Activities at AIMR
E-mail kotani[at]

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