Differential Geometry Seminar: Witten deformation on noncompact manifolds

Seminar | September 23 | 4-5 p.m. | 939 Evans Hall

 Xianzhe Dai, UC Santa Barbara

 Department of Mathematics

Motivated by considerations from the mirror symmetry and Landau-Ginzburg model, we consider Witten deformation on noncompact manifolds. Witten deformation is a deformation of the de Rham complex introduced by Witten in an influential paper and has had many important applications, mostly on compact manifolds. We will discuss some recent work with my student Junrong Yan on the spectral theory of Witten Laplacian, the cohomology of the deformation as well as its index theory.