### 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.