Speaker：Runlin Zhang（Peking University）

Time：2021-12-10  14:30

Location：Tencent Meeting ID：830629511（No Password）

Abstract:

Let Y be a Riemannian symmetric space of non-compact type and let p: Y —> X be a locally symmetric quotient of Y. The fibre of a point x in X under p is discrete and Eskin—McMullen find an asymptotic count of this discrete set with respect to the natural Riemannian metric on Y. Similarly, one can replace x by some other closed sub-manifold of X and ask for an asymptotic count. In this talk the sub-manifold we take is a horocycle and we will actually discuss a very special case of this problem. Such a count is achieved by studying translates of a homogeneous measure associated to this horocycle plus a volume computation.