Martin Bridson (University of Oxford)

Finite Shadows of Infinite Groups, Finiteness Properties, and Geometry

There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects. But how much understanding can one really gain about an infinite group by examining its finite images? Sometimes little, sometimes a lot. In this colloquium talk, it is sketched the rich history of this problem and describe how input from hyperbolic geometry and low-dimensional topology have transformed the subject in recent years.