We prove that $1-o(1)$ fraction of all $k$-SAT functions on $n$ Boolean variables are unate (i.e., monotone after first negating some variables), for any fixed positive integer $k$ and as $n$ tends to infinity. This resolves a conjecture by Bollobás, Brightwell, and Leader. The proof uses among others the container method and the method of (computer-free) flag algebras.
The lecture is summarizing results of a paper of Dingding Dong, Nitya Mani, and Yufei Zhao, and a follow-up paper with additional authors Bernard Lidický and the speaker.
The talk is aimed for a general audience, including computer scientists.