Michael Hitrik (UCLA)

The APDE seminar on Monday, 11/8, will be given by Michael Hitrik (UCLA) online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).

Title: Semiclassical asymptotics for Bergman projections: from smooth
to analytic

Abstract: In this talk, we shall be concerned with the semiclassical
asymptotics for Bergman kernels in exponentially weighted spaces of
holomorphic functions. We shall discuss a direct approach to the
construction of asymptotic Bergman projections, developed with A.
Deleporte and J. Sj\”ostrand in the case of real analytic weights, and
with M. Stone in the case of smooth weights. The direct approach
avoids the use of the Kuranishi trick and allows us, in particular, to
give a simple proof of a recent result due to O. Rouby, J.
Sj\”ostrand, S. Vu Ngoc, and to A. Deleporte, stating that, in the
analytic case, the Bergman projection can be described up to an
exponentially small error.