Algebraic Geometry Seminar

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Moduli Spaces of Curves and Teichmüller Dynamics

Speaker: Dawei Chen, Boston College

Location: Warren Weaver Hall 1314

Date: Tuesday, November 10, 2015, 3:30 p.m.

Synopsis:

An Abelian differential defines a Euclidean metric with conical singularities that can realize the underlying complex algebraic curve as a flat surface. Varying the shape of flat surfaces induces an action on the Hodge bundle over the moduli space of curves, called Teichmüller dynamics. A number of questions about geometry and dynamics on flat surfaces boil down to understanding their orbit closures in moduli spaces. This talk will be an introduction to Teichmüller dynamics as well as its applications to the geometry of moduli spaces, with a focus on a fascinating interplay between algebraic geometry, combinatorics, dynamics, geometric topology and number theory. Moreover, I will survey recent advances in the field, including the latest Fields Medal work of Mirzakhani et al.