This year’s summer school again consists of two parts. All information, including lecture notes, recordings will be available on the course homepage: https://www.ibs.re.kr/ecopro/summer-2024/

Week 1: July 29 — August 2

Lecturer: Boris Bukh (CMU)

Title: Algebraic methods in combinatorics

Description: The aim of this lecture series is to introduce algebraic proof techinques in extremal combinatorics. Three main topics will be covered: polynomial interpolation, slice rank and algebraic geometry constructions. Depending on pacing and audience’s wishes, towards the end, we might discuss other recent topics of interest.

Week 2: August 5 — August 9

Lecturer: Tung Nguyen (Princeton)

Title: Recent work on the Erdős–Hajnal conjecture

Abstract: A conjecture of Erdős and Hajnal asserts that every graph with a forbidden induced subgraph contains a clique or independent set of polynomial size. We will discuss recent work on this conjecture (joint with Alex Scott and Paul Seymour, and partly with Matija Bucić), which includes the loglog improvement over the general bound of Erdős and Hajnal, Rödl’s theorem and the polynomial Rödl property, and the method of iterative sparsification with application to prime graphs and graphs of bounded VC-dimension.