Limits of cubic differentials and projective structures by David Dumas

ORGANIZERS
Siddhartha Gadgil, Krishnendu Gongopadhyay, Subhojoy Gupta and Mahan Mj
DATE & TIME
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.

APPLICATION DEADLINE
31 July 2017
CONTACT US
sggs2017 ictsresin
PROGRAM LINK

0:00:00 Surface Group Representations and Geometric Structures
0:00:08 Limits of cubic differentials and projective structures
0:00:38 Joint work with Michael wolf
0:00:54 Calabi - Cheng - You correspondence (1975)
0:08:30 Theorem (Wolf - D 2015)
0:11:54 Example
0:13:15 Theorem (2000, Labourie, Loftin)
0:17:56 Main theorem
0:28:00 Local limit construction
0:29:43 1. Local about Pn
0:30:46 2. Ray case
0:33:22 3. Degree bound
0:37:56 Construction of local limit: Ray case
0:43:41 General case
0:48:48 Near and far
0:53:32 Suggest
0:54:34 Lemma
0:59:52 Outline of the proof
1:01:58 Note
1:08:47 Q&A