Complex Analysis seminar

The meetings are on Fridays from 11-12am in the seminar room of the Hamilton Mathematics Institute.

Please contact me at if you are interested.








Schedule-


26.09.25   Nikhil

Bergman kernels in the semiclassical limit I
Abstract: Given a Hermitian holomorphic line bundle on a complex Hermitian manifold, the Bergman projector is the projector from smooth sections of the bundle onto the holomorphic ones. The Bergman kernel is the Schwartz kernel of the projector. For tensor powers of the line bundle one is interested in the asymptotics of the Bergman kernel in the semiclassical limit as the power goes to infinity. This asymptotics can be derived using the sophisticated classical work of Boutet de Monvel-Sjostrand. As well as the analytic localization technique of Bismut-Lebeau and Dai-Liu-Ma-Marinescu. This talk will be a survey of these techniques.

10.10.25 Nikhil

Bergman kernels in the semiclassical limit II

17.10.25   Gian Maria Dall'Ara

The global irregularity phenomenon in the dbar-Neumann problem
Abstract: In this talk, I will discuss some work that I did in the last few years around the mysterious phenomenon of global irregularity in the dbar-Neumann problem, uncovered by M. Christ (building on the work of various others) in the 1990s. I will touch the following topics: 1) how finding a convenient setting for investigating the interaction of geometry and global regularity led us to using methods of o-minimal geometry (this is various joint works with S. Mongodi, B. Lamel, A. Berarducci, M. Mamino and S. Calamai) 2) how failure of compactness and global hypoellipticity emerges in (some) linear PDEs (this is in part joint with A. Martini) 3) what we still do not understand about the d-bar Neumann problem on worm domains (beyond Christ's work)


24.10.25   Dmitri Zaitsev

Introduction into the tower multitype.
Abstract: My plan is introduce the tower multitype following my recent paper (on arxiv) and my lecture notes available on https://www.maths.tcd.ie/~zaitsev/#research . I will discuss the relationship with other multitypes and their applications to regularity in the d-bar-Neumann problem.