Mathematical logic seminar - September 16, 2014

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


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 "measure-theoretic" 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 μ-a.e. hyperfinite connectedness relation and to construct examples of graphs which are hard to color.