University of Toronto's Symplectic Geometry Seminar

March 31, 2008, 2:10pm
Bahen 6183

Yuri A. Kordyukov

Russian Academy of Sciences, Ufa, Russia

Geodesic flows in transverse geometry of Riemannian foliations


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.