Event № 422
Geometric group theory arose from the study of periodic tilings of proper geodesic metric spaces, or equivalently the study of uniform lattices in isometry groups of such spaces. It provides a way to study finitely-generated infinite groups geometrically.
In joint work with Michael Björklund we propose a framework to study aperiodic tilings of proper geodesic metric spaces. This framework is based on three main ingredients:
1) Tao's notion of approximate subgroups (generalizing Meyer's notion of a model set in R^n)
2) Delone sets in locally compact groups
3) Classical geometric group theory
In this talk I will define the central notions of uniform and non-uniform approximate lattices arising in this framework, and explain some first steps towards a "geometric approximate group theory", i.e. a geometric theory of finitely generated (uniform) approximate lattice.