Andrey Kupavskii "Random restrictions and forbidden intersections"
Andrey Kupavskii from MIPT, Russia and CNRS, France will give the talk "Random restrictions and forbidden intersections" on the labs' Big Seminar.
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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.
Watch the video:
Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.