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Non archimedean representations of surface groups in PGL(3) and A2-Euclidean buildings

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 16, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Anne Parreau (Université de Grenoble I (Joseph Fourier))
Location: MSRI: Simons Auditorium
Tags/Keywords
  • surface group

  • length function

  • compact Riemann surface

  • tower structure

  • non-archimedean field

  • CAT(0) space

  • Fock-Goncharov coordinates

  • triangulation structures

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14229

Abstract

In this talk we study Fock-Goncharov generalized shearing parameters for representations of a punctured surface group in PGL(3,K) for an ultrametric field K, acting on the associated (real) Euclidean building.  The main motivation is to understand degenerations of real convex projective structures on surfaces.  We will explain how to interpret these parameters in the Euclidean building, using a geometric classification of triples of ideal chambers.  Under simple open conditions on the parameters, we construct a nice invariant subspace and an associated finite  A2-complex encoding the marked length spectrum. This allows to describe degenerations of convex projective strucures in an open cone of parameters.

Supplements
23395?type=thumb Parreau.Notes 514 KB application/pdf Download
Video/Audio Files

14229

H.264 Video 14229.mp4 370 MB video/mp4 rtsp://videos.msri.org/data/000/023/304/original/14229.mp4 Download
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