Séminaire Géométrie et groupes discrets

Discrete Subgroups with Lipschitz Limit Set

by Prof. Andrés Sambarino (CNRS & IMJ-PRG)

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons


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

In this talk we will focus on discrete subgroups Γ of higher rank Lie groups G whose limit set is a Lipschitz manifold, i.e. locally the graph of a Lipschitz map. This is a not-uncommon feature, verified by Zariski-dense groups, usually caused by stable geometric properties of the embedding Γ → G. We will recall several examples of such groups, specially those coming from Higher rank Teichmüller Theory. The main purpose of the lecture is to explain a recent result, in collaboration with B. Pozzetti and A. Wienhard, where we prove that the critical exponent of a specific combination of eigenvalues (only depending on the dimension of the limit set) is independent of the representation. We will also explore some of its consequences.

Organized by

Fanny Kassel