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.

A joint seminar with the Geometry & Topology Seminar series.