John Meakin: Combinatorial inverse semigroup theory
Combinatorial inverse semigroup theory
John Meakin, University of Nebraska-Lincoln
Inverse semigroups are algebraic objects that arise in the study of partial symmetry in mathematics in much the same way as groups arise in the study of symmetry. They have been studied extensively as algebraic objects in their own right, and in the context of their connections with several other areas of mathematics -- for example topology, combinatorial group theory and the theory of $C^\star$-algebras. Free inverse semigroups have a beautiful structure and there is a burgeoning theory of combinatorial inverse semigroups, i.e. a theory of presentations of inverse semigroups by generators and relations and a study of closed inverse subsemigroups of free inverse semigroups.
In this talk I will give an introduction to combinatorial inverse semigroup theory, with particular focus on the use of basic ideas from automata theory. I will also briefly indicate some applications to the study of Leavitt path algebras, subgroups of free groups and immersions between some classes of topological spaces.