Geodesic Growth in Groups

Alex Bishop (UTS)

Abstract

The concept of growth in finitely generated groups is well-studied with famous results including examples of groups with intermediate growth, and Gromov’s classification of groups with polynomial growth. In this talk, we will consider a similar problem known as geodesic growth. In particular, we will see a new result which is a step towards the classification of groups with polynomial geodesic growth and thus a step towards the search for a group with intermediate geodesic growth. Furthermore, we will show a formal language classification for the language of geodesic for finitely generated virtually abelian groups.