The Global Geometry of the Moduli Space of Curves

The guiding problem of algebraic geometry is to classify algebraic varieties up to isomorphism. In dimension 1 this problem is approached by considering the moduli space of curves (Riemann surfaces) of genus g. This space which is the universal parameter space for curves of genus g, is playing an increasingly important role in algebraic and arithmetic geometry as well as string theory.

I will review basic properties of the moduli space of curves and describe several fundamental problems related to its Kodaira dimension and cone of curves. I will also discuss recent work leading to a counterexample to the Harris-Morrisson Slope Conjecture on effective divisors on the moduli space of curves.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).