Title: Asymptotics of SL(3,R)-Hitchin representations along rays of cubic differentials
Speaker: Andrea Tamburelli (Rice University, USA)
Date: 27 March 2023
Time: 4:00 pm
Venue: MS Teams (online)
Hitchin’s theory of Higgs bundles associated holomorphic differentials on a Riemann surface to representations of the fundamental group of
the surface into a Lie group. We study the geometry common to representations whose associated holomorphic differentials lie on a ray.
In the setting of SL(3,R), we provide a formula for the asymptotic holonomy of the representations in terms of the local geometry of the differential.
Alternatively, we show how the associated equivariant harmonic maps to a symmetric space converge to a harmonic map to a building, with geometry
determined by the differential. All of this is joint work with John Loftin and Mike Wolf.