Winter school 2025

This year’s winter school is taking place on Jan 6-10, 2025. All information, including lecture notes, recordings will be available on the course homepage: https://www.ibs.re.kr/ecopro/winter-2025/

Lecturer: Huy Pham (IAS)

Recent developments in probabilistic combinatorics: New synergies

Recent developments in probabilistic combinatorics have brought about synergistic interactions across multiple disciplines, including extremal combinatorics, probability theory and theoretical computer science. This mini-course aims to give an introduction to some of these developments and interactions. 

In the first part of the mini-course, we will discuss the Kahn-Kalai conjecture on thresholds and expectation thresholds and its close relation to Talagrand’s selector process conjecture in probability theory. We will also touch on several subsequent developments of the proof technique in extremal combinatorics, probability theory and theoretical computer science. 

The Kahn-Kalai conjecture opens up a new avenue on thresholds of interesting properties in random graph models. Yet, while it relates thresholds to the expectation thresholds, estimation of the latter remains a highly challenging task in general. Recent developments have found close connections between this task and previous fundamental developments in extremal combinatorics, such as the regularity method. In the second part of the mini-course, I will briefly overview classical aspects of the regularity method before discussing its new applications to thresholds and other problems in probabilistic combinatorics.

Summer school 2024

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.

IBS Extremal Combinatorics and Probability Group
기초과학연구원 수리및계산과학연구단 극단 조합 및 확률 그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Extremal Combinatorics and Probability Group (ECOPRO)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: ecopro@ibs.re.kr, Fax: +82-42-878-9209
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