Analytic methods in graph theory

Joint School of Mathematics and ACO Colloquium
Friday, November 6, 2015 - 3:05pm for 1 hour (actually 50 minutes)
Skiles 005
Daniel Kral – University of Warwick
Robin Thomas

Please Note: Refreshments will be served in the atrium after the talk.

The theory of combinatorial limits provides analytic ways of representing large discrete objects. The theory has opened new links between analysis, combinatorics, computer science, group theory and probability theory. In this talk, we will focus on limits of dense graphs and their applications in extremal combinatorics. We will present a general framework for constructing graph limits corresponding to solutions of extremal graph theory problems, which led to constructing counterexamples to several conjectures concerning graph limits. At the end, we will discuss limits of sparse graphs and possible directions to unify the existing approaches related to dense and sparse graphs.