Algebra Seminar talk
2011-09-16
Jorge Almeida
Relatively free profinite semigroups
Abstract:
For their intimate connections with the theory of rational languages,
relatively free profinite semigroups have become a well-established
tool in many aspects of the theory and its applications, particularly
in the framework of Eilenberg-type algebraic classification schemes.
They serve as a powerful descriptive tool and, despite their rather
general tendency to be uncountable, they often provide a route to
decidability results. By focusing our attention on rich structural
entities, they also fit well into the solid ground of classical
Mathematics, opening at the same time doors to toolboxes and
drawing analogies with other areas, such as group theory, topology,
and dynamical systems.
The purpose of the talk is to introduce and put into (the author's) perspective recent results concerning relatively free profinite semigroups. They are all concerned with various structural aspects of free profinite semigroups over `large' pseudovarieties. Until recently, not much was known in such cases.