Prof. Filippo Cesi Universita' La Sapienza Roma Titolo: THE ALDOUS' SPECTRAL GAP PHENOMENON Mercoledi' 14 Novembre 2018 ORE 16:00 Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo, 1 - Pal.C - Aula 211 Abstract: Some families of Markov chains have a spectral gap which coincides with the spectral gap of an extremely simplified version of the chain. Another way of restating the same concept is: some families of Cayley graphs have a spectral gap which can be found in a very low dimensional representation of the underlying group. We will present a general approach which could be useful when going fishing for this phenomenon in an arbitrary finite group. Two specific examples will be discussed: the case of the symmetric group which corresponds to the "original" Aldous' spectral gap conjecture, proven in 2010 by Caputo, Liggett and Richthammer, and case of the Weyl group W(B_n) we studied in a recent paper.