**---------------------------------------- APPLICATIONS ARE CLOSED ------------------------------------------ **

**Organizing/Scientific Committee:** Emmanuel Breuillard (Univ. of Cambridge), Richard Canary (Univ. Michigan), Indira Chatterji (Univ. Nice-Sophia Antipolis), Fanny Kassel (CNRS-IHES)

The Summer school on "Aspects of Geometric Group Theory" will be held at the Institut des Hautes Etudes Scientifiques (IHES) from 8 to 19 July 2019. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

This school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

A group is a mathematical object encoding natural notions of symmetries and transformations. Geometric group theory is an area in mathematics devoted to the study of discrete groups by exploring connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act.

As a distinct area, geometric group theory is relatively new, and became an identifiable branch of mathematics in the early 1990s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, Lie groups and homogeneous spaces, algebraic topology, computational group theory, and differential geometry. There are also substantial connections with complexity theory, mathematical logic, dynamical systems, probability theory, K-theory, and other areas of mathematics.

Nowadays, geometric group theory is a very active and competitive area of research, as shown by the many conferences in the field but also several special programs such as an IHP program in 2014, a jumbo MSRI program in 2016 and a program at the Newton Institute in 2017 to name a few.

We will choose a few important trends in geometric group theory and teach those to graduate students across mathematical fields, so that young people in several areas of mathematics such as algebra, geometry, dynamics, or topology have some basics to either understand a few problems in geometric group theory, or use geometric group theory methods in their respective fields. Geometric group theory is a very broad area, and we will mainly focus on geometric aspects.

**INVITED SPEAKERS:**

So far the following people have agreed to give a mini-course:

- Yves Benoist
*(CNRS and Université Paris-Sud)* - Kai-Uwe Bux
*(Universität Bielefeld)* - Ruth Charney
*Brandeis University)* - François Dahmani
*(Université Grenoble Alpes)* - Anna Erschler
*(**CNRS and ENS)* - François Guéritaud
*(CNRS and Université de Lille)* - Kathryn Mann
*(Brown University)* - Yair Minsky
*(Yale University)* - Karen Vogtmann
*(University of Warwick)* - Genevieve Walsh
*(Tufts University)* - Anna Wienhard
*(Universität Heidelberg)* - Daniel T. Wise
*(McGill University)*

**This is an IHES Summer School, organized in partnership with the Clay Mathematical Institute, and the support of the Société Générale, the FMJH, the IUF, the ANR GAMME, the project Jeunes Géomètres, the National Science Foundation and the ERC.**