## Several Complex Variables Seminar

**Date:** September 20, 2017

**Time:** 2:00PM - 2:50PM

**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.