Daniel Kral: Graph limits and extremal combinatorics

Speaker: Daniel Kral

Title: Graph limits and extremal combinatorics

Abstract: Theory of combinatorial limits has opened new links between analysis, combinatorics, computer science, group theory and probability theory. In this theory, large dense graphs are represented by an analytic object called a graphon. Motivated by problems in extremal graph theory, we will focus on graphons that are uniquely determined by finitely many density constraints, so-called finitely forcible graphons. We will show that finitely forcible graphons can contain any computable graphon as a subgraphon. This result provides a unified framework containing several earlier ad hoc constructions of finitely forcible graphons. The talk is based on joint work with Jacob Cooper and Taisa Lopes Martins.