0124060 – Extremal Graph Theory

Welcome to the course! It consists of two parts dedicated to major Ramsey and Turán-type problems in modern Extremal Combinatorics. In the first half, we will mainly deal with the following question: ''what is the maximum number of edges in an n-vertex graph that does not contain some forbidden subgraphs?'' More specifically, we will prove the theorems of Mantel, Turán, Erdos-Stone, Bondy-Simonovits! In the second half, we will be looking for the ''order in an arbitrary large structure.'' More specifically, we will prove the famous Ramsey theorem and study its hypergraph, canonical, induced, and linear variants. You will learn how to use probabilistic method, stepping-up lemma, Szemerédi regularity lemma, dependent random choice, and much more! Lectures are held weekly starting from the 24th of October. Problem classes are held biweekly starting from the 28th of October. Attendance and homework are not compulsory (no credits) but highly recommended!