Heat Kernels, Topology, and Sub-Riemannian Geometry
Parallel parking is a frustrating and familiar example of Hamiltonian dynamics with an external constraint: you want your car to move left/right, but instead can only rotate it and move forward/backwards. The natural setting for these dynamics is sub-Riemannian manifolds, of which one of the simplest examples is a Contact manifold. In this talk I will discuss joint work with Pierre Albin, where we investigate the topology of such contact manifolds by studying the solution to the heat equation as a Riemannian metric degenerates to an intrinsic sub-Riemannian "metric". In this way, we hope to understand the topology and geometry of a Contact manifold due to the strong connection between the heat equation and the geometry and topology of a space. No knowledge of sub-Riemannian geometry, contact geometry, or heat kernels will be assumed.
Password: “arizona” (all lower case)