Program
Introduction to arithmetic groups and locally symmetric spaces
Student No.:50
Time:13:00-14:50, Dec 1, 2, 3 (Mon, Tue, Wed) and Dec 8, 9, 10 (Mon, Tue, Wed)
Instructor:Lizhen Ji  [University of Michigan]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2014-12-1
Ending Date:2014-12-10

 

 

Description:

Arithmetic subgroups of Lie groups such as SL(2, Z)  occur naturally in number theory, differential geometry, algebraic geometry, topology etc,  and they provide role model examples in geometric group theory. 

In these lectures, we will define and study basic properties of arithmetic subgroups of Lie groups, especially, arithmetic subgroups of semisimple Lie groups.

We will also study closely related arithmetic locally symmetric spaces, which are quotients of symmetric spaces by arithmetic subgroups, such as rigidity properties (Mostow strong rigidity and Margulis super-rigidity), and compactifications.

 

Reference:

Dave Witte Morris, Introduction to Arithmetic Groups, preprint of a book, 2014. 

M.S. Raghunathan, Discrete subgroups of Lie groups.  Springer-Verlag, 1972. 

L. Ji, Arithmetic groups and their generalizations. What, why, and how. American Mathematical Society & International Press, 2008.