In this two-week program, we explore the interactions between geometric group theory, geometric structures and Anosov representations. Geometric group theory, in the broadest sense, seeks to understand the structure of groups through their actions on objects with geometric meaning. Conversely, one can take a known group and attempt to understand all its geometrically meaningful actions. One natural notion that arises in this setting is an Anosov representation, which came about as an attempt to describe what it means for the action of a discrete group on a homogeneous space to be geometrically well behaved. Also, in his Erlangen program, Felix Klein viewed geometry as a space which is invariant under a group of transformations. This gave rise to the notion of a geometric structure, which gives yet another notion of a geometrically meaningful action of a group on a homogeneous space.
It is unsurprising that there are many interactions between the study of geometric group theory, Anosov representations, and geometric structures. The goal of this two-week meeting is to bring together researchers in these fields to encourage further collaboration.
An introductory workshop aimed at graduate students and young researchers will be conducted in the first week from 4 - 7 January. The goal of this workshop is to provide participants with the necessary background to start research in these three areas. Several mini-courses will be conducted in this workshop.
In the second week, from 12 - 15 January, there will be a conference. The talks will focus on hierarchically hyperbolic spaces, circle actions, the study of various geometric structures (such as Anti-de Sitter, complex hyperbolic, real hyperbolic, and affine geometry), Hitchin representations, and latest advances in the study of Anosov representations.