|Universiteit Faculteit FNWI English version||3 april 2007, e-mail|
Woensdag 11 april 2007
AbstractIt is often the case in mathematics that algebraic structures act as useful invariants for other types of structures. Finite state automata are basic models of computation and a long line of research, originating with Schutzenberger and Eilenberg, among others, has established semigroups as powerful invariant structures for studying these models.
In recent work with Jean-Eric Pin and Serge Grigorieff we have realised that the connection between semigroups and automata theory is a special case of Stone duality, another mathematical relationship between structures of very different nature. This realisation has allowed us to generalise the scope of the invariant theory and thereby obtain new results in automata theory.
In this talk I will introduce the basic structures involved. I will give some idea of the nature of duality theory, how it comes into play in the case of automata and semigroups, and indicate the type of results we have been able to obtain.