Thresholds - Jinyoung Park

Members’ Colloquium
Topic: Thresholds
Speaker: Jinyoung Park
Affiliation: Stanford University
Date: May 16, 2022
Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold.
In the first talk, I will introduce the Kahn-Kalai Conjecture with some motivating examples and then briefly talk about the recent resolution of the Kahn-Kalai Conjecture due to Huy Pham and myself.
In the second talk, I will discuss our proof of the conjecture in details.