Hypoelliptic Laplacian and the Trace Formula

Explore the intricacies of hypoelliptic Laplacians and trace formulas in this Distinguished Lecture Series presentation from the Institute for Mathematical Sciences. Delve into the heat equation method in index theory and its application to semisimple orbital integrals associated with the Casimir operator of reductive groups. Examine the geometric formula derived from this approach and its connection to Selberg's trace formula. Investigate the deformation of the Laplacian using Fokker-Planck operators, which bridges the gap between the Casimir operator and geodesic flow. Discover recent findings by Shu Shen and the speaker regarding the replacement of the Casimir operator with arbitrary elements from the center of the Lie algebra. Gain insights into advanced mathematical concepts and their applications in this hour-long lecture delivered by Jean-Michel Bismut from Université Paris-Saclay, France.