Séminaire Géométrie et groupes discrets

# Degenerations of SL(2,C) Representations and Lyapunov Exponents

## by Prof. Romain Dujardin (LPMA, Sorbonne Université)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

Let G be a finitely generated group endowed with some probability measure μ and $(\rho_{\lambda})$ be a non-compact algebraic family of representations of G into SL(2,C). This gives rise to a random product of matrices depending on the parameter λ, so the upper Lyapunov exponent defines a function on the parameter space. Using techniques from non-Archimedean analysis and algebraic geometry, we study the asymptotics of the Lyapunov exponent when λ goes to infinity. This is joint work with Charles Favre.

Organized by

Fanny Kassel

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