Time：13:30-14:30, Friday, March 6 2026
Venue：E14-212
Speaker: Weixia Zhu, University of Vienna
Title：Semi-classical heat kernel asymptotics on complex manifolds with boundary
Abstract：Let $M$ be a relatively compact open subset of a smooth $n$-dimensional complex manifold $M'$, whose closure $\overline{M}$ has smooth boundary $X$. Let $L^k$ be the $k$-th tensor power of a Hermitian holomorphic line bundle over $M'$. In this talk, I will discuss our recent results on the asymptotic expansion of the heat kernel associated with the $\bar{\partial}$-Neumann Laplacian acting on $L^k$-valued forms on $\overline{M}$ in the high tensor power limit $k \to \infty$. As an application, we obtain a heat kernel proof of the holomorphic Morse inequalities for compact complex manifolds with boundary. This is joint work with Chin-Yu Hsiao and George Marinescu.
