Gradients in groups and applications Seminar

Given a residually finite group G one can study the growth rate of various invariants attached to its subgroups of finite index e.g. homology with coefficients in Q or F_p, minimal number of generators, number of relations and so on. These growth rates have connections with diverse areas of mathematics: L^2 cohomology, measure preserving actions of G, profinite groups. In this talk I will survey the main results and central problems in this subject and discuss some recent progress.