Non archimedean representations of surface groups in PGL(3) and A2-Euclidean buildings
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: MSRI: Simons Auditorium
compact Riemann surface
37Pxx - Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45]
37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37P30 - Height functions; Green functions; invariant measures [See also 11G50, 14G40]
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.
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