Time:  12:30  13:30 
Room: 
Wean Hall 8220

Speaker: 
Clinton Conley Department of Mathematical Sciences Carnegie Mellon University 
Title: 
An introduction to Borel graph theory

Abstract: 
We discuss the theory of Borel graphs on standard Borel spaces, which has been a fertile topic of research in recent decades. While results in this purely Borel context are interesting on their own, we pay special attention to the "measuretheoretic" context in which the underlying space is equipped with a standard probability measure and null sets are discarded at one's fancy. Results in this setting have connections with a variety of areas of mathematics including graph limits, ergodic theory, and probability. Our particular goals for this talk, after defining various notions, are to show ease of coloring graphs with μa.e. hyperfinite connectedness relation and to construct examples of graphs which are hard to color. 