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# Events for September 20, 2017 from General and Seminar calendars

## Noncommutative Geometry Seminar

**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.

## Several Complex Variables Seminar

**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.

## Numerical Analysis Seminar

## Groups and Dynamics Seminar

**Abstract:** It is an open question if iterated monodromy groups of complex rational functions are amenable. Another open question is if groups generated by automat of polynomial activity growth are amenable. We prove that if the iterated monodromy group of a complex rational function is generated by an automaton of polynomial activity growth, then the group is amenable. At first, we show that orbital Schreier graphs of iterated monodromy groups are recurrent, by comparing the random walk on the graph with the Brownian motion on the associated Riemanian surfaces, Then we prove amenability of the group using techniques of extensive amenability. This is a joint work with K. Pilgrim and D. Thurston.

## AMUSE

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

**Location:** BLOC 628

**Speaker:** Yi Wang, Texas A&M University

**Title:** *On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains*

**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*

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Martin Licht

**Title:** *Smooth commuting projections in rough settings: Weakly Lipschitz domains and mixed boundary conditions*

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Volodymyr Nekrashevych, Texas A&M

**Title:** *Amenability of iterated monodromy groups for some complex rational functions*

**Time:** 6:00PM - 00:00AM

**Location:** 2nd Floor Patio

**Speaker:** Undergraduate Students, Texas A&M University, Department of Mathematics

**Title:** *Mathematics Undergraduate Research Expo*