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
Heiko Dietrich (Monash University, Australia) Computation with finitely-presented groups
Katherine Stange (University of Colorado Boulder, USA) Integral packings and Number Theory

Speakers (to be confirmed) for Week 1:
Martin R. Bridson (University of Oxford, UK)
Darren Long (University of California, Santa Barbara, USA)
Alexander Lubotzky (Weizmann Institute of Science, Israel)

These lectures are intended for graduate students and Post-Doctoral Fellows. The lecture series will be supplemented with problem sessions (with “TA support”).

Speakers of Conference in Week 2 (10–14 June 2024):
Jacques Audibert (Max-Planck-Institut for Mathematics in the Sciences, Germany)
Emmanuel Breuillard (Oxford University, UK)
Alla Detinko (University of Huddersfield, UK)
Simion Filip (University of Chicago, USA)
Alexander Hulpke (Colorado State University, USA)
Sang-hyun Kim (Korea Institute for Advanced Study, Korea)
Alex Kontorovich (Rutgers University, USA)
Emmanuel Kowalski (ETH Zürich, Switzerland)
Gaven Martin (Massey University, New Zealand)
Chen Meiri (Technion – Israel institute of Technology, Israel)
Andrei Rapinchuk (University of Virginia, USA)
N. Venkataramana (Tata Institute of Fundamental Research, India)

Speakers (to be confirmed) for Week 2:
Nir Avni (Northwestern University, USA)
Matthew Conder (The University of Auckland, New Zealand)
Martin Liebeck (Imperial College London, UK)
Peter Sarnak (Institute for Advanced Study and Princeton University, USA)

Public Lecture
Jordan Ellenberg (University of Wisconsin–Madison, USA) to be confirmed