The HADES seminar on Tuesday, November 1st will be at 3:30 pm in Room 740.

Speaker: Peng Zhou

Abstract: Let $(M, \omega)$ be a smooth compact Kahler manifold and $(L,h)$ a positive hermitian line bundle on $M$. Given a smooth real valued function $H$ on $M$, we may consider the Toeplitz quantization $T_{H,k}$ acting on $H^0(M, L^k)$. Let $[a,b]$ be an interval, the partial Bergman kernel is the orthogonal projection from $H^0(M, L^k)$ to sum of eigenspaces of $T_{H,k}$ with eigenvalue within $[a,b]$. We study the behavior of the projection kernel near the “boundary”. This was based on joint work with Steve Zelditch.