Geometry Seminar

Starting with the Unit Disk:

Why are Bounded Symmetric Domains

and their quotients interesting ?

Professor Ngaiming Mok

The University of Hong Kong



The unit disk, or equivalently the upper half plane, is the simply connected domain on which there is a homogeneous metric of constant negative Gaussian curvature, viz., the Poincaré metric.  By the Uniformization Theorem the universal covering of any Riemann surface other than a few exceptions is conformally equivalent to the unit disk.  For the study of Riemann surfaces it is therefore crucial to make use of the unit disk. At the same time the upper half plane is a natural parameter space for compact Riemann surfaces of genus 1, i.e., elliptic curves, and specific quotients can be interpreted as moduli spaces of elliptic curves with number-theoretic importance. The lecture is meant to be introductory and exploratory, moving from the unit disk to bounded symmetric domains together with their Bergman metrics, and explaining by way of a few examples that these domains and their quotients serve as the underlying spaces for interesting problems in Complex Analysis, Differential Geometry, Algebraic Geometry, Lie Theory and Number Theory.  The challenge is to understand the interplay among methods across a spectrum of areas of expertise, e.g., to use geometric methods to tackle number-theoretic problems in this context.



November 24, 2005 (Thursday)


4:00 – 5:00pm


Room 517, Meng Wah Complex



All are welcome