The University of Arizona
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Heat Kernels, Topology, and Sub-Riemannian Geometry

Analysis, Dynamics, and Applications Seminar

Heat Kernels, Topology, and Sub-Riemannian Geometry
Series: Analysis, Dynamics, and Applications Seminar
Location: ONLINE
Presenter: Hadrian Quan, Department of Mathematics, University of Illinois

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.

Zoom: https://arizona.zoom.us/j/99410014231
Password: “arizona” (all lower case)