Computational Aspects of Thin Groups

Overview

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.

Speakers of Lecture Series in Week 1 (3–7 June 2024):
Dane Flannery (University of Galway, Ireland) Computational aspects of strong approximation (Abstract, Slides 1,Slides 2, Slides 3, Problems, Problem Hints)
Heiko Dietrich (Monash University, Australia) Computation with finitely-presented groups. (Abstract, Materials for the lecture)
Katherine Stange (University of Colorado Boulder, USA) Integral packings and Number Theory (Abstract, Materials for the lecture)