# Ilaria Castellano will give a talk on the 20th of June

**Ilaria Castellano** (University of Milan-Bicocca) will talk about her work on the **20th of June** in **INB3305** at** 2:30 pm.**

Everyone is welcome to attend.

**Title:** Automorphism groups of regular trees: from the Euler-Poincarè characteristic to the double coset zeta-functions

**Abstract:** The Euler-Poincaré characteristic of a discrete group is an important (but also quite mysterious) invariant. It is usually just an integer or a rational number and reflects many quite significant properties. The realm of totally disconnected locally compact groups admits an Euler-Poincaré characteristic: surprisingly it is no longer just a number but it is a rational multiple of a Haar measure. A key source of totally disconnected locally compact groups consists of automorphism groups of locally finite graphs. Since the computation of the Euler-Poincaré characteristic of the automorphism group is quite gentle when the graph is a 2-coloured regular tree, I plan to use such groups as leading examples throughout the talk. In particular, I will show that the Euler-Poincaré characteristic turns out to be related to the value at -1 of a zeta-function.

Based on a joint work with Gianmarco Chinello and Thomas Weigel.

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