Equidistribution: number theory and dynamics

I will explain how methods from analytic number theory, automorphic forms and homogeneous dynamics can be used to prove versions of simultaneous equidistribution and the mixing conjecture on the modular curve or more generally quotients of quaternion algebras. As a protoype I consider two low-lying horocycles of different speeds and investigate under which conditions they equidistribute in the product of two modular curves.