
November 19, 2020
4:15 pm
-
5:15 pm
Zoom
Title: Geometric Schottky Problem
Speaker: Lizhen Ji - University of Michigan
Abstract: The notion of Riemann surfaces was introduced by Riemann in his thesis in 1851, and the moduli space M_g of compact Riemann surfaces of genus g was introduced by Riemann in his masterpiece on abelian functions in 1857. When g>1, M_g is not a locally symmetric space, but shares some intriguing similarities with it. The important Jacobian map embeds M_g into the Siegel modular variety A_g, a very important locally symmetric space.
The classical Schottky problem is concerned with the characterization of the image of M_g in A_g as an algebraic subvariety. In this talk, we will discuss metric properties of the image with respect to the locally symmetric metric of A_g, for example, about the metric distortion and the large scale geometry.