Pacific Institute for the Mathematical Sciences - PIMS

Essential normality of Bergman modules on egg domains

During 2005-2006, Arveson and Douglas formulated a challenging conjecture in multivariable operator theory regarding the essential normality of compressed shifts in the usual Hilbert spaces of analytic functions, say, Bergman spaces on strongly pseudoconvex domains. (Essential normality means normality modulo compact operators.) In this talk, after stating this conjecture, I will report on a joint work with Xiang Tang about the essential normality of Bergman spaces on several classes of egg domains. These egg domains are generalizations of the unit ball and are weakly pseudoconvex in general. If time permits, I will say a few words about a resulting K-homology index theorem and discuss p-essential normality (that is normality modulo p-summable operators).

Speaker biography: Mohammad Jabbari received his Ph.D. in Mathematics from Washington University in St. Louis in 2019 with a dissertation about the index theory of Toeplitz operators on algebraic spaces. He was then a postdoctoral researcher at Centro de Investigacion en Matematicas (CIMAT), and then a Senior Lecturer in the Department of Mathematics at Vanderbilt University. His background is in Electrical Engineering (BSc and MSc), and he worked as an antenna and radar engineer for three years. He is currently a lecturer in the Department of Mathematics at Rutgers University. In August 2023, he will be joining the University of Regina as a PIMS Postdoctoral fellow under the sponsorship of Prof. Martin Argerami.

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

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See past seminar recordings on MathTube.