Hamish Short (Université d’Aix-Marseille I)

Title: Introduction to the geometry of the word problem

Abstract: Starting in the 1980s from the seminal work of Gromov and Thurston, among others, geometric group theory has been a tool to study algorithmic problems related to infinite groups. Early in the 20th century, Max Dehn formulated the three classical problems in group theory: the word problem, the conjugacy problem and the isomorphism problem. This course is dedicated to the exposition of the geometric methods that have been developed to understand the first and most important of the three problems. This session will be dedicated to introduce some of the basic tools of the theory and their related results. In particular, in this session we will introduce van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups.