Representation stability and congruence subgroups

Andy Putman

An important structural feature of the kth homology group of SL_n(Z) is that it is independent of n once n is sufficiently large. This property is called 'homological stability' for SL_n(Z). Congruence subgroups of SL_n(Z) do not satisfy homological stability; however, I will discuss a theorem that says that they do satisfy a certain equivariant version of homological stability.