My research deals with some aspects of the curvature of a Riemannian manifold, in particular the way various curvature assumptions influence the topological properties. There are several groups of theorems that address this question, and my contribution belongs to Pinching Theorems. The method I used consists of studying special flow of metrics whose property is that the reduced curvature tensor changes according to the heat equation.

I have also employed the tools of Riemannian geometry (especially foliations on Riemannian manifolds) in order to study the properties of orbits of vector fields coming from various control theory problems.

In collaboration with Ernst Ruh and Maung Min-Oo, I have obtained new parametrization of the space of multivariate normal distributions (and a new distance formula) and am investigating futrher applications.