On the profinite rigidity of higher rank lattices
16:00 – 17:30
If two infinite groups have the same set of finite quotients, are they isomorphic or at least commensurable? This question is particularly intriguing for lattices in simple Lie groups. We show that in most higher rank Lie groups, there exist lattices with the same finite quotients that are not commensurable. But surprisingly, three exceptional Lie groups exhibit profinite rigidity: in the complex groups of type E_8, F_4, and G_2, the set of finite quotients determines the commensurability class of a lattice. Joint work with Steffen Kionke.