Remembrances of Gilbert

Abstract

Gilbert Baumslag was one of the leading infinite group theorists of the second half of the twentieth century. Through his own work, his students, and his mentoring, he had a profound effect on both the direction and interests in group theory. There is an ongoing seminar on his work given at Cornell University and various talks from this seminar can be found on the internet. The year he organized on combinatorial group theory at MSRI in 1989 ushered in much of the interest on automatic groups and hyperbolic groups. We note the paper by Alonso, Gersten, Shapiro, and Short explaining Gromov’s ideas on hyperbolic groups andwhich came out of that conference as one of foundational works in geometric group theory. Gilbert’s work and influence has been extremelywide, fromclassical combinatorial group theory, involving embedding theorems, and theory of nilpotent andone-relator groups to automatic andhyperbolic groups; the development of algebraic geometry over group with Myasnikov and Remeslennikov, which was instrumental in the proof of the Tarski theorems; the use of the variety of group representations with Peter Shalen; the development of groupbased cryptography. In addition to all this work in theoretical group theory, there was also his work on the Magnus project and all that it entailed in terms of computer implementations of group theoretic procedures. Since group theoretic procedures do not necessarily terminate, the Magnus project work as well as the work on group-based cryptography, veered greatly into computer science applications.