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## IHES Summer School 2019: Aspects of Geometric Group Theory

### July 8-19, 2019

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 1990's.
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 geometrical aspects.

### Speakers

So far the following people have agreed to give a mini-course:
Yves Benoist
Kai-Uwe Bux
Ruth Charney
François Dahmani
Pallavi Dani
Anna Erschler
François Guéritaud
Frédéric Haglund
Kathryn Mann
Yair Minsky
Karen Vogtmann
Genevieve Walsh
Anna Wienhard
### Organising/Scientific Committee

Emmanuel Breuillard

Richard Canary

Indira Chatterji

Fanny Kassel

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 and the
ERC.

C'est une école de l'IHES, organisée en partenariat avec le Clay Mathematical Institute,
avec le soutien de la Société Générale,
la FMJH, l'IUF,
l'ANR GAMME,
projet Jeunes Géomètres et
l'ERC.

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