Malcev presentations for subsemigroups of groups

A Malcev presentation is a special type of presentation for a semigroup that embeds in a group. Malcev presentations were introduced by J.-C. Spehner in 1977, but are related to earlier work by A.I. Malcev on the embeddability of semigroups into groups. They are important because a semigroup can admit a finite Malcev presentation but no finite 'ordinary' presentation. This talk will give an introduction to Malcev presentations and discuss various advances made over the last few years, including connections with automatic semigroups and the theory of formal languages more generally.