Robert Gilman, Stevens Institute of Technology

Abstract: The class of automatic groups was introduced in the late 1980's as an approximation to the class of fundamental groups of compact 3-manifolds. Automatic groups may be thought of as those finitely generated groups for which multiplication of an arbitrary group element by a fixed group element can be performed by a finite automaton. In this talk we will review the development of automatic group theory over the last two decades with emphasis on open problems.