Orbital Integrals and the Elliptic Cover

Speaker


Jean-Michel Bismut (University of Paris-Sud)
Date
Mon April 16th 2012, 4:00pm
Event Sponsor
Mathematics Research Center
Location
Building 380, Room 383N
MRC Event Series

 Orbital integrals and the elliptic cover If G is a reductive real Lie group, orbital integrals are key ingredient in Selberg’s trace formula. I will explain how one can think of the evaluation of semisimple orbital integrals for heat kernels as the computation of a Lefschetz trace. These orbital integrals are invariant under one specific hypoelliptic deformation. This gives an explicit expression for the orbital integrals. When descending the situation to a locally symmetric space, the spectrum of the original Casimir operator remains rigidly embedded in the spectrum of the hypoelliptic deformation. Finally, I will explain how, by providing us with an extra degree of freedom in deforming operators, we get rid of the “elliptic cover”.