Dynamics Seminar: Ilya Khayutin (Princeton / IAS) - CM Points, Joinings and Intermediate Measures

Tue, 02/01/201814:15-15:15
Ross 70
A celebrated theorem of Duke states that Picard/Galois orbits of CM points on a complex modular curve, e.g. SL2(Z)\SL2(R)/SO2(R), equidistribute in the limit when the absolute value of the discriminant goes to infinity. Michel and Venkatesh have conjectured that a sequence of some 2-fold self-joinings of CM orbits equidistributes in the product space as long as it escapes any closed orbit of an intermediate subgroup, i.e. Hecke correspondences.
I will present the relation between CM points and flows of diagonalizable groups and discuss the application of the joining rigidity theorem of Einsiedler and Lindenstrauss. The remaining obstacle to proving equidistribution is the potential concentration of mass on graphs of Hecke correspondences and translates thereof. I will introduce a method to discard the possibility of intermediate limit measures for diagonalizable actions where "linearization" is not applicable. This method can be useful when additional arithmetic structure is available.