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ESI Senior Research Fellow Program, fall term 2009/10
L2 Methods in Complex Analysis
Course of advanced graduate lectures by
Professor Jeff McNeal
(Ohio State University, Columbus, OH, USA)
October 28 - November 19 and December 9 - December 17: Wednesday 11:00 - 13:00 and Thursday 11:00 - 13:00
Seminars: tba, ESI, Schrödinger lecture hall
Abstract:
In this course I'll discuss how to use Hilbert space techniques to solve the Cauchy-Riemann equations on
domains in Cn and on complex manifolds. These techniques are quite flexible and
we will explore the variety of L2 estimates on the Cauchy-Riemann operator that are known
to exist, including the relatively recent "twisted" estimates. I'll also give many applications of these
estimates throughout the course. Some of the directions we'll apply the estimates to are: the boundary
behavior of the Bergman kernel, extension theorems of Ohsawa-Takegoshi type, compactness of the d-bar
Neumann operator, and the boundary behavior of biholomorphic mappings between domains in Cn.
ESI Senior Research Fellow Program coordinated by Prof. Joachim
Schwermer, Fakultät für Mathematik, Universität Wien,
Nordbergstraße 15, A-1090 Wien (Joachim.Schwermer@univie.ac.at).
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