Moduli space of abelian differentials and Teichmuller dynamics
Student No.:50
Time:Tue/Wed 13:00-14:50, 2016-07-05 ~ 2016-07-27
Instructor:Dawei Chen  [Boston College]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2016-7-5
Ending Date:2016-7-27



An abelian differential defines a flat metric with conical singularities such that the underlying Riemann surface can be realized as a plane polygon with certain parallel edge identification. Varying the shape of such polygon presentations induces a GL(2,R)-action on the moduli space of abelian differentials, called Teichmüller dynamics. A number of questions about geometry and dynamics on Riemann surfaces boil down to studying the GL(2,R)-orbit closures. What are their dimensions? Do they possess manifold structures? How can one calculate relevant invariants? In this course we will give an elementary introduction to Teichmüller dynamics, focusing on its beautiful interplay with algebraic geometry, arithmetic geometry, combinatorics, and geometric topology, as well as recent developments in the field, including the latest Fields Medal work of Mirzakhani et al.  







Riemann surfaces








1. Dawei Chen, Teichmüller dynamics in the eyes of an algebraic geometer, arXiv:1602.02260


2. Alex Wright: Translation surfaces and their orbit closures: An introduction for a broad audience, arXiv:1411.1827


3. Anton Zorich: Flat surfaces, arXiv:math/0609392


4. Anton Zorich: The Magic Wand Theorem of A. Eskin and M. Mirzakhani, arXiv:1502.05654