Arithmetic quantum unique ergodicity and measure rigidity

Nicolas Bergeron

October 23rd, 2002

Courant Institute of Mathematical Sciences New York University New York, NY

Abstract

1 Introduction

Let X be a ℝ or ℂ hyperbolic space. Over ℝ, X is a Riemannian manifold which is simply connected with constant sectional curvature K ≡ −1.

Over ℂ, but in the holomorphic setting (holomorphic Riemannian metric). For normalization purposes, we take K ≡ −4.

Goal: Understand Γ X.