** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2015.04.21, 15:00--17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Trees, currents and systems of
partial isometries."

**Speaker:** Arnaud Hilion
(Aix-Marseille Université)

**Abstract:**
Given a system of 1-dimensional partial isometries, I will explain how to define an "unfolding" induction that allows to describe the invariant measures of the systems. The most famous examples of such systems probably are interval exchange transformations. More generally, a free group acting by isometries on an \(\mathbb{R}\)-tree (so that the action is free and the orbits are dense) can be encoded by a system of partial isometries. In this case, one can show that the dual measures (or currents) to such a tree give rise to a simplex of finite dimension. This situation leads to consider the general setting of train-track towers. (The talk will be organized around joint work with N. Bédaride, T. Coulbois and M. Lustig.)