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Jeffery McNeal (The Ohio State University) is going to give a course on

« L2 methods in complex analysis »

as our Senior Research Fellow for the program. The lectures are held October 28 - November 19, 2009 each Wednesday: 11:00 - 13:00 & Thursday: 11:00 - 13:00, at the ESI Schrödinger Lecture Hall.

The december session is cancelled!

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.