Séminaire Géométrie et groupes discrets

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

by Prof. Romain Dujardin (LPMA, Sorbonne Université)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


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

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