Introduction to Teichmuller space, mapping class groups, and applications of moduli spaces
Student No.:50
Time:Thu/Fri 13:00-14:50, 2015-07-30 ~ 2015-08-28
Instructor:Lizhen Ji  [University of Michigan]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2015-7-30
Ending Date:2015-8-28



Teichmuller space and the action of mapping class groups on it were first used to study the moduli space of Riemann surfaces. But both Teichmuller space and mapping class groups have many other applications such as low dimensional topology, geometric group theory, and dynamics etc. There are also fruitful and beautiful analogy between the action of mapping class groups on Teichmuller space and the action of arithmetic groups on symmetric spaces.


In these lectures, we will give an introduction to  Teichmuller space,  mapping class groups, and moduli spaces or deformation of spaces are used in many other subjects.





B. Farb, D. Margalit, A primer on mapping class groups. Princeton Mathematical Series, 49. Princeton University Press, Princeton, NJ, 2012. xiv+472 pp.

L. Ji, A tale of two groups: arithmetic groups and mapping class groups. Handbook of Teichmuller theory. Volume III, 157–295, IRMA Lect. Math. Theor. Phys., 17, Eur. Math. Soc., Zurich, 2012.