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

par Prof. Romain Dujardin (LPMA, Sorbonne Université)

lundi 7 oct. 2019, 14:30 → 15:45 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.