This blog is written by the participants in the “Berstein Seminar” MATH 7520, Spring 2015 at Cornell University. The seminar is led by Timothy Riley. Participants take it in turns to present material in the seminar and then to write it up here. Participants also serve as editors for each other’s posts.
Gilbert Baumslag, who died in October 2015, was an outstanding figure in the subject. The idea of the course is to 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. The blog is titled exploring the works of Gilbert Baumslag, but might equally have been titled exploring combinatorial and geometric group theory through the works of Gilbert Baumslag, as for some of the participants the course is a first encounter with these areas.
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.