Clinton Conley : An introduction to Borel graph theory II

Mathematical logic seminar – September 23, 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 II

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 “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.

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