## University of Sydney Algebra Seminar

# Nick Gill (University of Bristol)

## Friday 2nd July, 12.05-12.55pm, Carslaw 175

### Growth in solvable subgroups of GL_r(p)

The study of "growth in groups" centres around the following question: given a set A inside a group G with group operation *, how big is A*A or A*A*A? This innocuous looking question has generated huge interest in the last few years with some spectacular results of Helfgott, Tao, Green, Breuillard, Pyber, Szabo and others. What is more "growth results" have been used by people like Bourgain, Gamburd, and Sarnak, to construct expander graphs, and to "sieve".

We focus on growth inside solvable subgroups of GL_r(p) - the group of r by r matrices over a field of prime order. We are able to reduce the question of growth in this setting to the study of p-groups in GL_r(p).

This is joint work with Harald Helfgott.