A proof of the Kahn-Kalai conjecture

Kahn and Kalai conjectured that the threshold of an increasing property is always within a logarithmic factor of the expectation threshold, a quantity often much easier to compute. The Kahn-Kalai conjecture directly implies a number of difficult results in probabilistic combinatorics. I will discuss recent joint work with Jinyoung Park that resolves the Kahn-Kalai conjecture. Time permitting, I will discuss some applications of the new argument.