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.
Date & Time
May 16, 2022 | 2:00pm – 3:00pm
LocationSimonyi Hall 101 and Remote Access
Video link: https://www.ias.edu/video/thresholds