Geometric Group Therapy Seminar

Speaker: Antoine Goldsborough

Title: Random walks and quasi-isometries

Abstract: In this talk, I will start by introducing random walks on groups as well as some notions in geometric group theory. As we will see these, random walks and quasi-isometries do not usually interact very well with each other. To remedy this, one needs to introduce a more general notion of Markov chains. With these new objects, we manage to prove results about the behaviour of random walks up to quasi-isometry. Pushing the study further, I will discuss a new quasi-isometry invariant based on randomness with which we can build groups with exotic properties.