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Title: Moduli space of Riemann surfaces and Teichmueller dynamics
Speaker: Prof. Dawei Chen (Boston College)
Abstract:
An abelian differential defines a flat structure on the underlying Riemann surface, such that it can be realized as a plane polygon. Varying the shape of the polygon induces an SL(2,R)-action on the moduli space of differentials, called Teichmueller dynamics. In this lecture series, I will give an elementary introduction to Teichmueller dynamics from the viewpoint of algebraic geometry.
In the first lecture I will introduce basic definitions and properties of moduli spaces of Riemann surfaces, of abelian differentials and the SL(2,R)-action.
In the second lecture I will introduce several examples of special SL(2,R)-orbits, including Hurwitz spaces of torus coverings and Teichmueller curves. Their study is related to the classical Hurwitz counting problem from a combinatorial viewpoint.
The third lecture will focus on the interplay between dynamical properties of SL(2,R)-orbits and intersection theory on moduli space. If time allows, I will also explain some recent breakthroughs as well as open problems in this field.
Place: Room 210, Math Science bldg.
Date: 11:00-12:30 August 25-27 2014
Contact: Prof. Donghoon Hyeon ( dhyeon@postech.ac.kr)
Hyemin Shin ( hyemin@postech.ac.kr, Tel. 279-8021)
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