Speaker: Tzvika Shemtov (Tel-Aviv University): Title: Rank gradient of sequences of subgroups in a direct product Abstract: The Reidemeister-Schreier process shows that the number of generators of any finite index subgroup U of a finitely generated group G is at most (d(G)-1)[G : U] + 1. We define the rank gradient of a sequence G_i of finite index subgroups of a finitely generated group G to be inf_i (d(G_i) - 1)/[G : G_i] thus measuring the strictness of the aforementioned inequality. We will prove that excluding few trivial cases, the rank gradient of sequences in direct products is zero. This is a joint work with Nikolay Nikolov and Mark Shusterman.