EVENT DETAILS AND ABSTRACT

Title: Higher Laminations and Affine Buildings
Speaker: Ian Le
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

Let S be a surface. We are interested in studying the space X_{G,S}, the space of G-bundles on S, for G a split-real semi-simple Lie group, with framing at the boundary.

When G=SL_2, X_{SL_2,S} is a version of Teichmuller space. One tool in understanding Teichmuller space is the theory of laminations, which were invented by Thurston in the study of two- and three-dimensional topology. The remarkable work of Fock and Goncharov shows that the space of laminations is the tropical points of X_{SL_2,S}. They go further to suggest that there should be a space of laminations for all G, given by the tropical points of X_{G,S}, but they do not give a geometric definition of higher analogues of laminations.

Inspired by work of Parreau and others, I will show that the tropical points of higher Teichmuller space have an interpretation in terms of affine buildings, and that this gives the correct geometric definition of higher laminations. This gives a Thurston-like compactification of higher Teichmuller space. If there is time, I will talk about some duality conjectures due to Fock and Goncharov, and how my constructions give rise to a conjectural canonical basis.

For the pre-talk, I will explain as much as I can of the classical case G=SL_2, and also try to give some intuition as to what an affine building is.