11-12 December 2017
Université Pierre et Marie Curie Paris 6
Europe/Paris timezone

Hypoelliptic deformation, self-adjointness, and analytic torsion

12 Dec 2017, 09:30
50m
Amphi Astier (Université Pierre et Marie Curie Paris 6)

Amphi Astier

Université Pierre et Marie Curie Paris 6

4, place Jussieu 75252 Paris Cedex 05

Speaker

Prof. J.-M. Bismut (Université d'Orsay)

Description

The purpose of the talk is to explain the construction of non self-adjoint Hodge Laplacians, which naturally deform classical Hodge theory. If X is a compact Riemannian manifold, let X be the total space of its tangent bundle. The deformed Hodge Laplacian is constructed over X. It is a hypoelliptic operator on X, which is essentially the sum of a harmonic oscillator and of the generator of the geodesic flow. In the real case, the symplectic form of X is used in its construction. Applications to analytic torsion, real and holomorphic, will be given. Time permitting, connections with Selberg's trace formula will be explained.

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