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Compactifications of spaces of maximal representations and non archimedean geometry

Presented by: 
Marc Burger
Monday 19th June 2017 - 10:00 to 11:00
INI Seminar Room 1
Maximal representations form certain components of the variety of Sp(2n,R)-representations of
a compact surface group. These components coincide with Teichmueller space for SL(2,R). As in
the case of SL(2,R), one can use length functions to compactifiy these components thereby generalizing the
Thurston boundary of Teichmueller space. We will present recent results concerning the structure of
these boundaries and the properties of the length functions forming them.

The general picture that emerges is that this boundary decomposes into a closed subset formed of length
functions vanishing on subsurfaces or associated to R-tree actions with small stabilizers, and an open complement
on which the mapping class group acts properly discontinuously. The latter part of the boundary is non empty if and
only if n is at least 2.

The approach is based on the study of an  analogue of maximal representations over ordered, non archimedean fields.

This is joint work with A. Iozzi, A. Parreau and B. Pozzetti.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons