Algebra and Logic Seminar - 8/3/2016

Tuesday, 8 March 2016, 2:00 p.m.

Lecturer: Alan Cain (CMA, FCT-UNL)

Title: "Markov semigroups"

Local: Sala de seminários, Edifício VII

Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: Mikhail Gromov defined a group as "Markov" if it admits a prefix-closed regular language of unique representatives with respect to some generating set. All groups that are hyperbolic (in Gromov's sense) are Markov. This seminar will survey the natural generalization of this concept to semigroups and monoids. Various interesting examples will be presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It will also describe the interaction of the class of Markov semigroups and other "nice" classes of semigroups, such as commutative semigroups, subsemigroups of virtually abelian or polycyclic groups, and hyperbolic semigroups. It will briefly survey how the closure (or otherwise) of the class of Markov semigroups under direct products, free products, and finite-index subsemigroups and extensions.
A large part of the research descibed here is joint work with Victor Maltcev.