Upcoming Seminars

Title: Complex Dynamics of Rational Maps
Seminar: Analysis and Differential Geometry
Speaker: Ylli Andoni of Emory University
Contact: Shanshuang Yang, syang05@emory.edu
Date: 2022-12-06 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
We will look at the iteration of rational functions of one complex variable and study the behaviour of points in the complex sphere under such iterations. Such iterations split the plane into two sets, that of well-behaved and that of ill-behaved points known as the Fatou set and the Julia set respectively. The notion of equicontinuity will be used to formally define these two sets and we will relate this to normality as well. Properties of the Fatou and Julia sets will be looked at and topological consequences will be established as well.
Title: Sumset Estimates in Higher Dimensions
Seminar: Combinatorics
Speaker: David Conlon of Caltech
Contact: Liana Yepremyan, liana.yepremyan@emory.edu
Date: 2022-12-07 at 3:00PM
Venue: MSC W301
Download Flyer
Abstract:
We will describe recent progress, in joint work with Jeck Lim, on the study of sumset estimates in higher dimensions. The basic question we discuss is the following: given a subset A of d-dimensional space and a linear transformation L, how large is the sumset A + LA?