Tuesday, February 26th, 2008
10:00am - 11:00am, in Wheatley 2-123

Nilufer Koldan

Northeastern University

Semiclassical Asymptotics on Manifolds with Boundary

Abstract: In 1982 E. Witten introduced a deformation of the de Rham complex of differential forms on a compact closed manifold $M$ using a Morse function $f$ and a small parameter $h$. Witten's Laplacian can be defined in the same way as the usual Laplacian but by using Witten's deformed differential instead of the standard de Rham differential. In the semiclassical asymptotics of the eigenvalues of Witten's Laplacian, only small neighborhoods of the critical points of $f$ play a role. On a manifold with boundary, Witten's Laplacian can be defined in the same way, but we need to specify its domain. I will define a specific domain and will show that for this particular operator, all the interior and some of the boundary critical points play a role. I will write a model operator by considering the operator only around those points and this will lead us to the semiclassical asymptotics of Witten's Laplacian on manifolds with boundary.