Hypoelliptic Laplacian and the trace formula
IMS Distinguished Lecture SeriesHypoelliptic Laplacian and the trace formula
Jean-Michel Bismut
Université Paris-Saclay, France
The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Similar methods can be developed to give a geometric formula for semisimple orbital integrals associated with the Casimir operator of a reductive group, this computation being related to Selberg’s trace formula. The analogue of the heat equation method is a suitable deformation of the Laplacian by a family of Fokker-Planck operators that interpolates between the Casimir operator and the geodesic flow. Finally, we will explain results obtained by Shu SHEN and ourselves when the Casimir operator is replaced by an arbitrary element of the center of the Lie algebra. Receive SMS online on sms24.me
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