News

From July 1 to August 31, 2025, the Extremal Combinatorics and Probability Group (ECOPRO) at the Institute for Basic Science (IBS), Korea, successfully hosted its Summer Research Program. The program brought together outstanding undergraduate and graduate students from multiple universities, engaging them in two months of intensive study and research in combinatorics, graph theory, discrete geometry, and related areas.

During the program, participants systematically studied frontier research literature and took part in focused discussions and research projects under the guidance of ECOPRO members. Through regular seminars and academic exchanges, students deepened their understanding of extremal combinatorics and achieved substantive progress on specific problems.

In addition, ECOPRO organized a series of high-level lectures and small-scale workshops, inviting experts in the field to share recent research developments. These activities provided valuable opportunities for participants to broaden their academic perspectives and engage with the international research frontier. The program maintained a vibrant and rigorous academic atmosphere, fostering sustained interest in fundamental theoretical research.

The successful completion of this summer program not only continues ECOPRO’s tradition of nurturing young researchers, but also further strengthens its role as an international platform for academic exchange. The IBS ECOPRO group looks forward to organizing similar programs in the future, attracting talented students passionate about combinatorics and contributing to the advancement of the field.

The Korean Student Combinatorics Workshop (KSCW) aims to provide a platform for Korean graduate students, undergraduate students, and postdoctoral researchers studying combinatorics to build professional networks, share their research interests, and foster collaborative research.

The 2026 Winter Korean Student Combinatorics Workshop (KSCW 2026 Winter) will be held from February 2 to 6, 2026, at Shilla Stay Yeosu, with support from IBS ECOPRO.

All information is available on the workshop homepage: https://kscw.combinatorics.kr/2026w/

This year’s winter school is taking place on Jan 19-23, 2026. All information, including lecture notes, recordings will be available on the course homepage: https://www.ibs.re.kr/ecopro/winter-2026/

Lecturer: Eero Räty (IBS ECOPRO)

Recent advances in cut-problems on graphs

This mini-course will serve as an introduction to cut problems in graphs and related topics. The course will begin by covering the basics of spectral graph theory, including the Alon–Boppana theorem and the expander mixing lemma. We will then introduce some fundamental tools in the field, such as the Goemans–Williamson algorithm, along with its applications to various types of max-cut problems in graphs and hypergraphs. Towards the end of the course, we will explore recent advancements in the area, which rely on more involved spectral properties of adjacency matrices.

Up to 3 senior researchers. For more details, see https://www.ibs.re.kr/prog/recruit/eng/sub04_01/view.do?pageIndex=1&searchCondition=&searchKeyword=&idx=1971

The 1st Early Career Workshop in Extremal Combinatorics will be held on October 20–30, 2025 at IBS headquarter, Daejeon, Korea. For more details, see the page: https://www.ibs.re.kr/ecopro/1st-early-career-workshop-in-extremal-combinatorics-2025/

With Joonkyung Lee, we organize a workshop on Discrete Analysis at Yonsei University in Seoul. For more details, see https://sites.google.com/yonsei.ac.kr/days

Invited speakers

• Jineon Baek (Yonsei U.)
• David Conlon (Caltech)
• Seonghyuk Im (KAIST/IBS ECOPRO)
• Jaehoon Kim (KAIST)
• Sam Mattheus (VU Brussel)
• Huy Tuan Pham (IAS)
• Bjarne Schülke (IBS ECOPRO)
• Tibor Szabó (FU Berlin)
• Semin Yoo (IBS DIMAG)
• Yi Zhao (Georgia State U.)

Organizers

• Joonkyung Lee, Yonsei University
• Hong Liu, IBS

This year’s summer school is taking place on July 28-August 8, 2025. All information, including lecture notes, recordings will be available on the course homepage: https://www.ibs.re.kr/ecopro/summer-2025/

Location: Room B332, IBS, Daejeon
Zoom: 3469344087, PW: 2025

Lecturers:
Lior Gishboliner (University of Toronto): Around removal lemmas
Yuval Filmus (Technion): Introduction to Boolean Algebra

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.