Algebra Learning Seminar

Ty Ghaswala, Pure Mathematics, University of Waterloo

"If you love a group, set it free."

The existence of algebraic topology (even if you claim to know nothing about it) should be enough to convince you that doing topology without group theory is difficult, frustrating, alcoholism inducing, and above all, a disservice to topology.  In this talk I hope to convince you, at least for a moment, that thinking about groups while ignoring topology is a disservice to group theory.

I will be talking primarily about free groups, following the ideas in Stallings' paper "Topology of Finite Graphs."  Along the way I will show that free groups are residually finite, and time permitting, I will sketch proofs of classical results like Howson's theorem and Marshall Hall's theorem.

Everything will be defined from the ground up, and no algebraic topology knowledge will be assumed.  I swear.