Minicourse: Synergies of probabilistic and extremal combinatorics.

Time:

Venue/Location: Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi

Schedule: 

MWF, August 5 – Friday August 9: 9-11AM: Lectures. 

Tu, Th August 6 and 8, 9-11AM : Tutorials.   

Tu, Th, 14-16h: Open discussion.

Objective:

Probabilistic and extremal combinatorics are central branches of modern combinatorics. In probabilistic combinatorics, one attempts to study properties and phenomena around random discrete structures, such as random graphs, and draw insights from them. Surprisingly, while the main problems in extremal combinatorics are inherently about non-random large discrete systems, probabilistic insights have offered fruitful perspectives there, leading to powerful paradigms that exploit surprising ways in which structure and randomness interact. The regularity method is a cornerstone of this paradigm and has found influential applications across combinatorics and other areas, including probability, computer science, and number theory. The lectures aim to introduce participants to important developments in probabilistic and extremal combinatorics, including an introduction to the regularity method and its classical applications.

Recently, developments in probabilistic combinatorics and random graph theory, including the proof of the Kahn-Kalai conjecture on thresholds, have brought about new applications of the regularity method and related techniques in the study of random graphs. We will discuss some recent developments in probabilistic combinatorics around thresholds, and how the regularity method becomes crucial in applications of these developments.

Expected participants and requirements for participants

Prerequisite: graph theory and discrete probability. Familiarity with probabilistic methods and extremal combinatorics would be helpful.

Format: Hybrid (Zoom link will be available for participants from outside Hanoi only)

Language: English

Registration: click Here

Deadline for registration: August 1, 2024.

Contact: Mr. Le Hung Hai, Email: lhhai@viasm.edu.vn