Program
Introduction to Higher Teichmueller Theory
Student No.:50
Time:Tue/Wed 15:10-17:00, 2016-03-15~ 2016-04-06
Instructor:Qiongling Li  [Aarhus University & Caltech]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-3-15
Ending Date:2016-4-6
 

Description:

 

Higher Teichmueller theory brings together three apparently unrelated mathematical objects: geometric structures, representation varieties and Higgs bundles.

The G-character variety of surface group is the collection of representations of surface group in G up to conjugation. Higher Teichmueller theory is the study of such surface group representations for general G and related dynamics. When G is real split, Hitchin introduced a natural component in the G-character varitety in terms of Higgs bundles which has been known as the Hitchin component

I will start with basic concepts such as (G,X)-structures, principal bundles, flat connections and Higgs bundles. Then I will mainly introduce the Hitchin component for SL(3,R) as an example.
 

Prerequisite:

 

Differential geometry

 

 

Reference:

 

W. Goldman, Convex Real Projective Structures on Compact Surfaces, J. Differential Geometry 31 (1990), pp. 791 − 845.

J. Loftin, Affine spheres and convex RP^n -manifolds, American Journal of Mathematics, April, 123 ( 2001), No.2, pp. 255 − 274.

N.J.Hitchin, Lie groups and Teichmueller space, Topology 31 (1992), no. 3, 449–473. 

N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1