March 31, 2008, 2:10pm

Bahen 6183

Abstract:We will introduce classical and quantum analogues of the geodesic flow on the leaf space of a Riemannian foliation on a compact manifold as well as the noncommutative geodesic flow associated with the corresponding spectral triple (in the sense of noncommutative geometry of A. Connes). We will describe some relationships between these objects, which are based, in particular, on Egorov's theorem for matrix valued transversally elliptic operators on Riemannian foliations. Some related topics such as noncommutative symplectic geometry and symplectic reduction will be discussed.