Talk 6: Joint equidistribution: arithmetic and L-functions

A classical set of equidistribution problems concerns torus orbits of growing discriminants inside projective units of quaternion algebras. Examples include Heegner points or closed geodesics on the modular surface, integral points on ellipsoids, and supersingular reduction of CM elliptic curves.  A new generation of equidistribution problems, motivated by the mixing conjecture of Michel and Venkatesh, considers torus orbits inside pairs of quaternion algebras which in special cases has a rather concrete arithmetic description. I will show how automorphic forms and L-functions shed light on such questions.