Speaker
Description
The hypoelliptic Laplacian provides a deformation of an elliptic Laplacian to a family of hypoelliptic operators acting on the total space of a vector bundle. The deformation is specific to the geometry being deformed.
If G is a reductive group of non-compact type, the construction of the hypoelliptic Laplacian is done using the Dirac operator of Kostant. The semi-simple orbital integrals associated with the Casimir operator can be shown to be invariant under the hypo elliptic deformation, by a method that treats such orbital integrals as an index. The deformation can be used to give an explicit geometric formula for these orbital integrals.
In the talk, I will explain general features of the hypoelliptic Laplacian, and explain its applications to orbital integrals and to Selberg's trace formula.
