01/10/2008 22 e 29 de Outubro de 2008, 15:00-16:30, Sala B1-01
These talks will give an introduction to and an overview of automatic semigroups. Starting from the definitions, the basic theory of automatic semigroups will be discussed. We will see that while some of the elegant properties of automatic groups generalize to semigroups, others do not. We will discuss the two responses to this: trying to find other (perhaps less elegant) properties that do generalize to automatic semigroups, and investigating automaticity for restricted classes of semigroups that are in some way "group-like", such as completely simple semigroups or group-embeddable semigroups.
We will also look at the interaction of automaticity and semigroup constructions, decision problems for automatic semigroups, and some connections with other areas of algebra. Various open problems will be discussed.