2019-06-20 来源：数学科学研究中心

Abstract: There are two basic moduli spaces, the moduli space M_g of compact Riemann surfaces of genus g, and the moduli space A_g of principally polarized abelian varieties of dimension g. The period (or Jacobian) map connects naturally these two spaces \pi: M_g --> A_g. A_g is a complete noncompact locally symmetric space, and the map \pi induces a length metric on M_g. In this talk, I will discuss some results on the metric distortion of the map \pi and the large scale geometry of the induced length metric on M_g.