My research field is geometry, especially the influence of the curvature to various properties of the space. This area has strong connections with analysis and probability theory. Active interdisciplinary researches include the relation between curvature and the behavior of heat propagation, the geometric structures of spaces consisting of probability distributions, etc. Among them, optimal transport theory, gradient flows of convex functions, and information geometry have tight connections with machine learning as well as information theory. Upon mathematical strengths on these areas, we would theoretically contribute to the field of machine learning.
Optimal transport theory
Gradient flows of convex functions