Synopsis

MATH 7520 is on areas of combinatorial and geometric group theory, particularly as feature in the works of Gilbert Baumslag.

We will use Baumslag's writings as a starting point for an introduction to an assortment of topics in combinatorial and geometric group theory. We will explore what some of his achievements were, the influence his research has had, why he was interested in what he was, what open questions remain, and in what directions the various threads may develop next.

Topics are likely to include residual properties of groups, the Hopfian property, one-relator groups, parafree groups, finiteness properties, metabelian groups and embedding theorems, Marshall Hall's theorem, fibre products, algorithmic decidability, automatic groups, group theoretic cryptography, and applications of HNN-extensions. Open problems and examples will be emphasized.

It is a seminar in which all take turns to present. The only prerequisite is a willingness to participate. We will attempt to cultivate good presentation skills and we present write-ups of our lectures through a blog.