Gemma Crowe

Conjugacy, languages and groups

Formal language theory has found surprising applications in geometric group theory in recent years. One historical example was found by Cannon in hyperbolic groups, where geodesics were studied in order to find the nature of the standard growth series of hyperbolic groups. In this talk we will introduce languages associated to conjugacy classes. This will lead us to define the conjugacy growth series of a group, which compared to standard growth is in general a far more mysterious series! By studying properties of these languages, we will explore what this might tell us about conjugacy growth. Finally, we will consider if and when these properties can extend via quasi-isometries, including recent work on virtual graph products.