Miroslav Englis (23/04/15)

Benedikt Magnússon, April 19, 2015

Math Colloquium

Speaker: Miroslav Englis, Mathematics Institute, Prague & Opava, Czech Republic
Title: High-power asymptotics of weighted harmonic Bergman kernels

Location: Naustið, Endurmenntun, VR-II, 158.
Time: Thursday, April 23, at 11:00-12:00.

Abstract:

The asymptotics of the weighted Bergman kernels with respect to the weight \(|r|^\alpha\), where \(r\) is a defining function for a smoothly bounded strictly pseudoconvex domain and \(\alpha\to+\infty\), play prominent role in mathematical physics (Berezin quantization) as well as in complex geometry (Donaldson’s balanced metrics); the standard tool for their derivation is the famous description of the boundary singularity of the Bergman kernel due to Fefferman, combined with a construction due to Forelli and Rudin. The talk will describe why it is noteworthy to study the analogous asymptotics also for the Bergman kernels for harmonic functions, and will give a complete answer for the case of radial weights on the ball and horizontal weights on the upper half-space. The proofs actually proceed by relating the problem to the holomorphic case mentioned above, but on a different domain.