Seminar Event Detail


RTG Seminar on Geometry, Dynamics and Topology

Date:  Wednesday, November 01, 2017
Location:  3866 East Hall (4:00 PM to 5:30 PM)

Title:  An introduction to Hitchin representations

Abstract:   A representation from a closed surface group into PSL(n,R) is Hitchin if it can be continuously deformed to the composition of a Fuchsian representation into PSL(2,R) and the irreducible representation of PSL(2,R) into PSL(n,R). Labourie used dynamical techniques to show that Hitchin representations are "geometric." In particular, they are discrete, faithful, quasi-isometric embeddings.
In doing so, Labourie associates to each Hitchin representations a limit map from the boundary of the surface group into the space of n-dimensional flags and a splitting into invariant line bundles of the associated flat bundle over the geodesic flow of the surface. Sambarino showed how to associate a family of Anosov flows to a Hitchin representation which record "lengths" associated to simple roots of PSL(n,R). We will survey this theory and discuss some applications of Labourie and Sambarino's work. This talk will hopefully provide preparation for the talks of Tengren Zhang and Giuseppe Martone in upcoming weeks.

Files:


Speaker:  Richard Canary
Institution:  U Michigan

Event Organizer:   Spatzier   

 

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