Category Archives: Uncategorized

Introduction Last class, wonderfully recounted by Michaela, we learned about hyperbolic groups and defined the terms quasi-isometry and quasi-isometric. Importantly, we showed that there is a quasi-isometry between any group and its Cayley graph, and that two Cayley graphs of … Continue reading →

Hyperbolic Groups The next thrust of the course is hyperbolic groups. We care about hyperbolic groups for four reasons: In many models of “random groups,” groups are hyperbolic with probability 1. For example, under the few-relators model of random groups, … Continue reading →

Introduction This Friday we went international with a captivating lecture on the Grigorchuk Group and its good buddies given by guest lecturer Professor Rachel Skipper all the way from École Normale Supérieure in Paris! The Automorphisms of the Infinite Binary Rooted … Continue reading →

We left off our discussion of regular languages with dashed hopes when we learned that is a regular language if and only if is finite. This means that dealing with , the set of words on the generators of which … Continue reading →

Introduction Last class we discussed normal forms, which was wonderfully recapped in this Wednesday’s blog post by Akash. Today we will pretend that we are computer scientists and focus on languages and automata. Although it may seem a bit random … Continue reading →

Serre’s Property FA Welcome to Week 5! I can believe we’re halfway done with this class! We ended Wednesday’s class on free products with a claim : if and is finite, then is conjugate to a subgroup of or . … Continue reading →

On Friday, Professor Alden Walker gave a lovely talk on the Baumslag-Solitar Groups. I was fascinated by the Cayley graph of . Also, he discussed geodesics between group elements (a shortest but not necessarily unique! path in its Cayley graph … Continue reading →

Today we discussed a new way to combine two groups: the Free Product, and looked at the Cayley Graph of such products which led us to discuss Bass-Serre Trees. The Free Product of Groups Definition. Let and be groups. The … Continue reading →