The Goldman symplectic form on the Hitchin component by Tengren Zhang

Описание

SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES

DATE: 27 November 2017 to 30 November 2017

VENUE:Ramanujan Lecture Hall, ICTS Bangalore
The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classical Teichmüller theory may be viewed as a starting point of the subject, and following the work of Labourie and Goldman, many exciting developments have taken place when the target group is SL(n, R). Recent work of Kapovich, Leeb and Porti have connected the subject with geometric group theory and higher rank symmetric spaces, opening up new horizons. The aim of this discussion meeting is to expose all these recent developments on the subject and to understand avenues for further directions. The program is an immediate follow up to the ICTS Advanced School: Geometry, Groups and Dynamics-2017.

CONTACT US
sggs2017 ictsresin
PROGRAM LINK
https://www.icts.res.in/discussion-meeting/SGGS2017

Table of Contents (powered by https://videoken.com)
0:00:00 Start
0:00:07 The Goldman symplectic form on the Hitchin component
0:00:34 The PSL(V) - Hitchen component
0:04:12 Definition
0:06:44 Labouni
0:08:17 Goldman symplectic form
0:13:22 Q: What does w look like on Hit(S)?
0:17:38 Results
0:24:14 Theorem 1
0:26:37 Definition A (T,T) pulled sector field
0:28:14 Bunohan-Duggar
0:30:54 Modify
0:31:32 Theorem 2
0:33:48 Claim - is a linear bijection
0:38:32 What are the (T, J)- parallel flows?
0:40:57 Complete Flag
0:43:51 When
0:45:49 Projective transformations
0:48:27 Notation
0:48:58 First family of flows
0:53:12 Elementary emption flows
0:56:54 Proposition
0:58:49 Idea perform elementary emption and shearing flow using ideal triangles and edges of T
1:05:07 To prove theorem 1
1:14:56 Q&A