Video Lectures

Ratner's landmark equidstribution results for unipotent flows have had dramatic applications in many mathematical areas. Recently there has been considerable progress in the long sought for goal of getting effective equidistribution results for...

(Joint with Samuel Grushevsky, Gabriele Mondello, Riccardo Salvati Manni) We determine the maximal dimension of a compact subvariety of the moduli space of principally polarized abelian varieties Ag for any value of g. For g<16 the dimension is g−1, while for g≥16, it is determined by the larged dimensional compact Shimura subvariety, which we determine. Our methods rely on deforming the boundary using special varieties, and functional transcendence theory.