Workshop
Hilbert geometry over non-Archimedean ordered fields
- Xenia Flamm (MPI-MiS Leipzig, Germany)
Abstract
Convex projective surfaces arise as a geometric interpretation of Hitchin representations in SL(3, R). Their Hilbert metric encodes important information about the representation. Understanding degenerations of convex projective structures on a surface naturally leads to the study of the Hilbert geometry of subsets of the projective plane over a non-Archimedean ordered field. The goal of this talk is to introduce Hilbert geometry over such fields, and to show that degenerations of convex projective structures can in fact be viewed as length functions for these Hilbert metric spaces. This is joint work with Anne Parreau.