[Cancellation due to weather-related flight delays.  Talk to be rescheduled.]

The asymptotic expansion for the Bergman kernel has
important applications in complex analysis. Short-time asymptotic
expansion of the heat kernel played an important role in spectral
geometry. We will present our work on Feynman diagram formulas for
the coefficients in the asymptotic expansion of Bergman and heat
kernels on Kahler manifolds and their applications.