Dejan Govc: Topological connectivity of random permutation complexes

In one of the previous seminars, I talked about permutation complexes and their topology. A recent preprint from 2024 by Meshulam and Moyal showed that, for any fixed r ≥ 0 such complexes are asymptotically almost surely topologically r-connected, as n (the number of letters) tends to infinity. Their result also establishes some precise asymptotics for the probability of r-connectivity. I will present their work.