The classical de Rham theorem computes the cohomology of a smooth manifold by the de Rham complex. Introduced by Witten in an extremely influential paper, Witten deformation is a deformation of the de Rham complex. Its study on closed manifolds has produced a whole range of beautiful applications, such as direct analytic proof of the Morse inequalities and Bismut-Zhang's proof of Cheeger-M\"uller Theorem (also known as Ray-Singer Conjecture). Indeed, Witten deformation gives a direct bridge between geometry, topology and analysis.
Motivated by the Landau-Ginzburg model in mirror symmetry, the study of Witten deformation on noncompact manifolds is starting to attract more attention and becoming more important. We will introduce the classical results and survey some of our recent work, joint with Junrong Yan, in this direction.
[Meeting ID: 928 7488 3705 - Passcode: tensor]