Length spectrum compactification of the SL(3,R)-Hitchin component

Length spectrum compactification of the SL(3,R)-Hitchin component

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Andrea Tamburelli, Rice University
Fine Hall 314

Higher Teichmuller theory studies geometric and dynamical properties of surface groups representations into higher rank Lie groups. One of these higher Teichmuller spaces is the SL(3,R)-Hitchin component, a connected component in the SL(3,R)-character variety that entirely consists of faithful and discrete representations that are the holonomies of convex real projective structures on a surface. In a joint work with Charles Ouyang, inspired by Bonahon's interpretation of Thurston's compactification of Teichmuller space by means of geodesic currents, we describe the length spectrum compactification of the SL(3,R)-Hitchin component.  We interpret the boundary points as hybrid geometric structures on a surface that are in part flat and in part laminar.