Outline of lecture

Title: Geometry of the mapping class group.
Abstract:
The mapping class group of a surface is the group of diffeomorphisms of the surface, up to isotopy. This group is of interest to people working in a variety of different fields in which surfaces are important, such as geometric topology, algebraic geometry and certain areas of mathematical physics. We will give an introduction to the mapping class groups of surfaces, and related objects such as the complex of curves and Teichmuller space. We will survey some recent developments in understanding the large scale geometry of theses spaces, and consider some results in detail as time permits.