Families of automorphic forms on definite quaternion algebras and Teitelbaum's conjecture

The main goal of this note is to describe a new proof of the "exceptional zero conjecture" of Mazur, Tate and Teitelbaum. This proof relies on Teitelbaum's approach to the L-invariant based on the Cerednik-Drinfeld theory of p-adic uniformisation of Shimura curves