An introduction to the hypoelliptic Laplacian
主 题: An introduction to the hypoelliptic Laplacian
报告人: Jean-Michel Bismut (Professor of Mathematics, University of Paris XI, France)
时 间: 2013-10-10 17:00-18:00
地 点: Lecture Hall, Second Floor, Jia Yi Bing Building, 82 Jing Chun Yuan, PKU (Distinguished Lecture Series)
If X is a Riemannian manifold, the Laplacian is a second order elliptic operator on X. The hypoelliptic Laplacian Lb is an operator acting on the total space X of the tangent bundle of X, that is supposed to interpolate between the elliptic Laplacian (when b → 0) and the geodesic flow (when b → +∞). Up to lower order terms, Lb is a weighted sum of the harmonic oscillator along the fibre TX and of the of the geodesic flow. One expects that, in the deformation, there are conserved quantities. In the talk, I will describe three applications of the hypoelliptic Laplacian: The case of the circle. Selberg's trace formula and the evaluation of orbital integrals. A Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology
