## PIMS/UBC Distinguished Colloquium: Jean-Michel Bismut (U. Paris-Sud, Orsay)

- Date: 09/23/2011
- Time: 15:00

Jean-Michel Bismut (U. Paris-Sud, Orsay)

University of British Columbia

The hypoelliptic Laplacian

If X is a Riemannian manifold, the Laplacian is a second order elliptic operator on X. The hypoelliptic Laplacian L_b is an operator acting on the total space of the tangent bundle of X, that is supposed to interpolate between the elliptic Laplacian (when b -> 0) and the geodesic flow (when b -> \infty). Up to lower order terms, L_b is a weighted sum of the harmonic oscillator along the fibre TX and of the generator of the geodesic flow. In the talk, we will explain the underlying algebraic, analytic and probabilistic aspects of its construction, and outline some of the applications obtained so far.

PIMS, Zinovy Reichstein

Jean-Michel Bismut was born in 1948. He is a Professor of Mathematics at University Paris-Sud (Orsay), and a member of the Academie des Sciences, of the Academia Europaea, and of the Deutsche Akademie Leopoldina.

He received his 'Doctorat d'Etat' from Universite Paris VI in 1973 for his work in the control of stochastic processes. His interests in probability theory led him to study refinements of the index theorem of Atiyah-Singer.

Through his work on Quillen metrics, he participated to the proof of a Riemann-Roch theorem in arithmetic geometry. He constructed an exotic Hodge theory, whose corresponding Laplacian is a hypoelliptic operator on the cotangent bundle of a Riemannian manifold. Recently, he used the hypoelliptic Laplacian to give a new approach to the evaluation of orbital integrals.

Jean-Michel Bismut was a plenary speaker at the International Congress of Mathematics in Berlin in 1998, and a vice-president of International Mathematical Union (I.M.U.) from

2002 to 2006.

For further information please vist the event page at http://www.math.ubc.ca/Dept/Events/index.shtml?period=future&series=all