School of Mathematics & Physics, University of Lincoln
On the 29th of May 2019, during his research visit to the Charlotte Scott Centre for Algebra, Dominik Francoeur (University of Geneva) gave a talk on “Free subsemigroups in automata groups”. Dominik’s visit from the 28th of May till the 8th of June 2019 is supported by a London Mathematical Society Research in Pairs grant.
Abstract: “Despite being described by simple combinatorial objects, automata groups can sometimes possess striking or unusual properties. Indeed, one can find among this class infinite finitely generated periodic groups, groups of intermediate growth and just-infinite groups. In light of this, it is natural to wonder how the properties of the group are influenced by the properties of the underlying automaton. In this talk, after reviewing the basics of automata groups, we will investigate one such connection, namely the link between reversibility of the automaton and the existence of a free (non-abelian) semigroup. This is joint work with Ivan Mitrofanov.”