Geometry in the Presence of Symmetries
I enjoy working on problems in Riemannian geometry which involve Lie groups and group actions. In particular, I like to consider questions in spectral geometry. That is, I am interested in the extent to which one can “hear” the geometry of a Riemannian manifold. Recently, I have also started to think about problems concerning Riemannian submersions and manifolds of nonnegative curvature. If you are an undergraduate or graduate student with an interest in conducting research in geometry I would be more than happy to discuss projects with you and/or to suggest some background reading.
  • Applications of representation theory to dynamics and spectral geometry, Ph. D. Thesis, University of Michigan, Ann Arbor, MI USA 48104, 2001. (Advisor: Ralf Spatzier )