|Introduction to Teichmuller space of surfaces|
|Time：||Mon/Wed 10:10-12:00, 2016-07-18 ~ 2016-08-29（No lectures on Aug. 15 and 17）|
|Instructor：||Feng Luo [Rutgers University]|
|Place：||Conference Room 1, Floor 1, Jin Chun Yuan West Building|
This is an introduction to the Teichmuller space of Riemann surfaces and their applications to low-dimensional geometry and topology.
The moduli space of Riemann surfaces is a meeting ground for mathematical disciplines ranging from algebraic geometry, geometric topology, string theory and many others. It first appeared in the work of Riemann who computed its dimension. Rigorous constructions of the moduli space and the Teichmueller theory were given in the 1960s by Ahlfors and Bers in the setting of complex analysis and by Mumford in the setting of algebraic geometry.
We plan to cover the following topics: basic hyperbolic geometry and Riemann surfaces, coordinates of the Teichmuller spaces, Nielsen-Thurston’s classification, Thurston’s compactification of the Teichmueller space, and some of the recent work of M. Mirzakhani on moduli spaces.
Complex analysis and basic topology
1] Farkas, H & Kra, I., Riemann Surfaces (2nd ed.), Springer-Verlag
 Forster, O., Lectures on Riemann surfaces. Graduate Texts in Mathematics, 81. Springer-Verlag, New York, 1991
 Simon Donaldson, Riemann surfaces, Oxford Graduate Texts in Mathematics, 22, Oxford University Press, 2011
 Farb, B. and Margalit, D., A Primer on Mapping Class, Princeton University Press, 2011