Colloquium: Witten deformation on non-compact manifolds

Speaker: Xianzhe Dai, University of California, Santa Barbara

Abstract: The Morse theory, connecting topology and dynamics, has led to profound mathematics such as Bott's periodicity and Smale's proof of the higher dimensional Poincare conjecture. The Witten deformation introduced in an extremely influential paper by Witten gives rise to further enrichment of the theory and led directly to the development of Floer homology. Development in mirror symmetry, in particular the Calabi-Yau/Landau-Ginzburg correspondence has highlighted the importance of mathematical study of Landau-Ginzburg models. This leads to a whole range of questions on the Witten deformation on non-compact manifolds. In this talk we will discuss our joint work with Junrong Yan, on the L2-cohomology, the heat asymptotic expansion and the local index theorem in this setting.

Host: Yanli Song

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00 - 3:00 pm.