Program
An introduction to Anosov representations
Student No.:50
Time:Tue/Thu 13:00-14:50, 2017-07-04~2017-07-27
Instructor:Tengren Zhang  [California Institute of Technology]
Place:Conference Room 4, floor 2, Jin Chun Yuan West Building
Starting Date:2017-7-4
Ending Date:2017-7-27
 

The class on July 25 has been canceled.

 

 

Description:

 

 

I will give an introduction to the theory of Anosov representations. These are a particular class of representations from hyperbolic groups to reductive Lie groups that have ``good geometric properties”. One should think of the Anosov property as a generalization of the notion of convex cocompactness in the setting of rank 1 Lie groups to higher rank Lie groups. There will be a focus on examples, which include Hitchin representations, maximal representations, and holonomies of convex real projectice structures on closed hyperbolic manifolds.

 

 

 

Prerequisite:

 

 

Some basic Lie theory, hyperbolic geometry, and theory of smooth manifolds. Understanding the notion of (G,X)-structures will help, but is not required.

 

 

 

Reference:

 

 

F. Labourie; Anosov flows, Surface Groups and Curves in Projective Space; Inventiones Mathematicae 165(1) (2006), pp 51-114.

 

O. Guichard, Anna Wienhard; Anosov representations: domains of discontinuity and applications; Inventiones Mathematicae 190(2) (2012), pp 357-438.

 

M. Kapovich, B. Leeb, J. Porti; Morse actions on discrete groups on symmetric spaces, arXiv:143.7671

 

F. Gueritaud, O. Guichard, F. Kassel, A. Wienhard; Anosov representations and proper actions; Geometry and Topology 21 (2017), pp 485-584.