Andrey Kupavskii "Random restrictions and forbidden intersections" | Big Seminar

It is our pleasure to share the Big Seminar talk "Random restrictions and forbidden intersections" by Andrey Kupavskii.

Abstract:
Random restrictions is a powerful tool that played a central role in the breakthrough result by Alweiss et al. on the famous Erdos-Rado sunflower conjecture. In this talk, I will describe a new approach to getting a junta-type approximation for families of sets based on random restrictions. Such approximations have several exciting consequences, and I will present a couple of them. The first one is an upper bound on the size of regular k-uniform intersecting families similar to the one obtained by Ellis, Kalai and Narayanan for intersecting families under a much stronger restriction of being transitive. The second one is significant progress on the t-intersection (and the Erdos-Sos forbidden one intersection) problem for permutations. Improving and simplifying previous results, we show that the largest family of permutations [n] → [n] avoiding pairs of permutations with intersection exactly t-1, has size at most (n-t)!, for t polynomial in n. Previously, this was only known for fixed t.
Joint work with Dmitriy Zakharov.

Seminars schedule and archive are available here - http://combgeo.org/en/events/big-seminar.