Matthew Tointon

Nilpotent approximate groups

The classical Freiman-Ruzsa theorem states that a set of integers of small doubling closely resembles a multidimensional arithmetic progression. In this talk I will explain how to generalise this statement to a set of small doubling inside an arbitrary nilpotent group. In particular, I will incorporate a very recent development that makes the bounds independent of the nilpotency class of the ambient group.