Computational Aspects of Thin Groups

Arithmetic groups have long been of interest in number theory (e.g. via the theory of automorphic forms), geometry (e.g. building interesting examples of Riemannian manifolds), and topology (e.g. computing (co)homology of locally symmetric spaces). Yet, their subgroup structure, particularly of their infinite index subgroups, remains mysterious. Thin groups are such infinite index subgroups that have come to prominence recently because they arise naturally in various contexts with connections to number theory, geometry and topology. The focus of our two-week event is on computational aspects of thin groups. The recent activity highlights the need for algorithms and procedures to study these groups. Our event is the first aimed specifically at addressing this topic.