Dynamical Systems Seminar

In this talk I will discuss some recent results concerning the generalized Farey sequence. While these sequences arise naturally in the study of discrete (and in particular thin) subgroups, they can be used to describe interesting number theoretic sequences – for example rationals whose continued fraction partial quotients are subject to congruence conditions. Using methods from homogeneous dynamics we show that these sequences equidistribute and that the local statistics converge. Moreover a connection to Ford circle configurations allows us to extract very detailed information concerning the gap distribution and Gauss-Kuzmin statistics for one particular example of such a sequence.