Department of
Applied
Mathematics

Analytic representation of large graphs

Dan Kral

Abstract

The recently emerged theory of combinatorial limits has opened new links between analysis, combinatorics, computer science, group theory and probability theory. Combinatorial limits give an analytic way of representing large discrete objects. In the talk, we focus on limits of (dense) graphs. We will particularly focus on graph limits that are uniquely determined by finitely many density constraints; such limits are closely linked to problems coming from extremal graph theory. We will present counterexamples to two conjectures posed by Lovasz and Szegedy on the structure of the topological space of typical vertices of such graph limits.

The talk will be self-contained and no previous knowledge of the area will be assumed.