For a subset A of a finite-dimensional vector space over a finite field, It is known that 2A-2A must contain a subgroup of density that is quasi-polynomial in the density of A. We show an analogue result for the special linear group over a finite field, except we achieve a polynomial density for the subgroup. The main tool used is a new hyper-contractive estimate for the special linear group, that has origins in the study of 2-to-2 games.
This video was produced by the Simons Institute, and forms part of the workshop Structural Results.
