Laurent Michel, Stanford and Université Nice

The Analysis and PDE Seminar will take place on Monday, February 13, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Laurent Michel

Title: On the small eigenvalues of the Witten Laplacian

Abstract: The Witten Laplacian, introduced (by E. Witten) in the early 80’s to give an analytic proof of the Morse inequalities, also models the dynamics of the over-damped Langevin equation. The understanding of the so-called metastable states goes through the description of its small eigenvalues. The first result in this direction was obtained in 2004 (Bovier-Gayrard-Klein, Helffer-Klein-Nier) under some generic assumptions on the landscape potential. In this talk, we present the approach of Helffer-Klein-Nier and show some recent progress to get rid of the generic assumption.