Analysis and PDE Seminar: On the small eigenvalues of the Witten Laplacian.

Seminar | February 13 | 4:10-5 p.m. | 740 Evans Hall

 Laurent Michel, Stanford and Université Nice

 Department of Mathematics

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.