The exact $k$-SAT threshold for large $k$

We establish the random $k$-SAT threshold conjecture for all $k$ exceeding an absolute constant $k(0)$. That is, there is a single critical value $c_*(k)$ such that a random $k$-SAT formula at clause-to-variable ratio $c$ is with high probability satisfiable for $c c_*(k)$, and unsatisfiable for $c c_*(k)$. The threshold $c_*(k)$ matches the explicit prediction derived by statistical physicists on the basis of the one-step replica symmetry breaking (1RSB) heuristic. In the talk I will describe the main obstacles in computing the threshold, and explain how they are overcome in our proof.
Joint work with Jian Ding and Allan Sly.