My research subject is geometry, especially differential geometry and geometric analysis related to analysis and probability theory. A keyword of my research is “curvature” which represents how the space is curved. As seen in the difference between the sums of interior angles of triangles in a plane and a sphere, the behavior of the curvature influences various properties of the space (the shapes of triangles, the volume growth of concentric balls, how heat propagates, the behavior of entropy, etc.). This powerful and versatile conception has been applied to Riemannian manifolds, metric spaces, Finsler manifolds, Banach spaces, as well as discrete objects such as graphs.