Topics at the Interface of Low Dimensional Group Actions and Geometric Structures

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.