Program
Introduction to symmetric and locally symmetric spaces
Student No.:50
Time:Wed./Fri. 13:00-14:30
Instructor:Lizhen Ji  [University of Michigan]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building; Exception: July 4 and 11, Conference Room 1, Floor 1
Starting Date:2012-7-4
Ending Date:2012-8-10

Course description:

Spaces of constant curvature such as the Euclidean space, the sphere and the Hyperbolic plane are familiar to many people. Their importance comes from a rich supply of symmetries (or isometries) and quotient spaces. Many questions about quotients of these spaces are still open.

A natural generalization of these spaces consist of symmetric spaces, which was single-handedly developed by the great E. Cartan. Symmetric spaces and their quotients by discrete isometry groups, called locally symmetric space, provide some of the most important spaces in mathematics, occurring as special Riemannian manifolds, classifying spaces in topology, moduli spaces in algebraic geometry and number theory. In this course, we will give an introduction to all these topics by starting from basics.

 

Prerequisite:

Differential geometry and some group theory.