### Geometric approximate group theory

Geometry and Topology Seminar

19th March 2024, 2:00 pm – 3:00 pm

Fry Building, 2.04

An approximate group is a subset of a group that is "almost closed" under multiplication. Finite approximate subgroups play a major role in additive combinatorics. Recently Breuillard, Green and Tao established a structure theorem concerning finite approximate subgroups and used this theory to reprove Gromov’s polynomial growth theorem. Certain infinite approximate groups also are also classic well studied objects. For instance, nice approximate subgroups of R^n are models for mathematical quasi-crystals. Recently, Björklund and Hartnick have begun a program investigating infinite approximate lattices in locally compact second countable groups using geometric and measurable structures. In the talk I will introduce infinite approximate groups and present a new approach to studying these groups geometric group theoretic methods. This is joint work with Tobias Hartnick and Vera Tonić.

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