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Several Complex Variables Seminar

Fall 2017

Date:September 20, 2017
Time:2:00pm
Location:BLOC 628
Speaker:Yi Wang, TAMU
Title:On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains
Abstract:We show that under a mild condition, a principal submodule of the Bergman module on a strongly pseudoconvex domain, generated by a holomorphic function defined on a neighborhood of its closure, is p essentially normal for p>n. Two main ideas are involved in the proof. The first is that a holomorphic function defined in a neighborhood 'grows like a polynomial'. This is illustrated in a key inequality that we prove in our paper. The second is that commutators of Toeplitz operators behave much better than the operator themselves. This seminar is joint with the Non-Commutative Geometry Seminar.

Date:September 29, 2017
Time:1:50pm
Location:BLOC 628
Speaker:Gerardo Mendoza, Temple University
Title:TBA (joint with MPHA Seminar)

Date:October 13, 2017
Time:11:00am
Location:BLOC 220
Speaker:Blake Boudreaux, TAMU
Title:The Boundary Behavior of Biholomorphic Maps: An Example by B. L. Fridman
Abstract:This expository talk follows a construction by B. L. Fridman of two bounded domains in C^2 that are biholomorphically equivalent to the unit bidisc (and hence each other), but no biholomorphism between the domains can extend continuously to the boundary. This shows that there is no straightforward generalization of the classical theorem of Carathéodory to higher dimensions.