Geometric semigroup theory is the systematic
investigation of finitely-generated semigroups using the
topology and geometry of their associated automata. In this
talk I will discuss how a number of easily-defined
expansions on finite automata lead to simplifications of the corresponding semigroups. In particular that every finite
semigroup can be finitely expanded so that the right Cayley
graph of the expansion closely resembles the right Cayley
graph of a free Burnside semigroup.
Sponsored in part by the FCT approved projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER and by FCT through Centro de Matemática da Universidade do Porto. Also sponsored in part by FCT, the Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III, and by Caixa Geral de Depósitos.