Differential Geometry and Topology

course: Aspects of Teichmuller theory

speaker: Francois Labourie (Université Paris-Sud 11, Orsay, Paris)

abstract: In these two talks, I will present

1) An overview of some aspects of classical Teichmuller Theory. I will explain in the first talk how this theory can be thought of as a dictionary between various fields of mathematics:

complex geometry of curves hyperbolic geometry dynamics of the action of the fundamental group on the boundary at infinity representations of surfaces groups in PSL(2,R) combinatorics of trivalent graphs

2) How this extends (at least partially or conjecturally) when we replace 2 (in PSL(2,R)) with n (as in PSL(n,R)) in what seems now to be called "Higher Teichmuller Theory" with the works of Hitchin, Fock-Goncharov and myself completing some pages of the above dictionary. I will try to explain furthermore a result explaining how the theory survives when n goes to infinity. This is the purpose of my second talk.

timetable:
Tue 26 Oct, 10:00 - 11:15, Sala Conferenze Centro De Giorgi
Wed 27 Oct, 11:15 - 12:15, Sala Conferenze Centro De Giorgi
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