Jinyoung Park (박진영), Thresholds 1/2
July 18 Monday @ 4:30 PM - 5:30 PM KST
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 on Monday, 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 on Tuesday, I will discuss our proof of the conjecture in detail.