Group actions in geometric/arithmetic Combinatorics

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

The research project will explore the role and interaction of different types of symmetry in the combinatorial growth phenomena. Group action as the onset of growth has become a major research theme in the past 10 years. However, current technique is largely qualitative and seldom enables one to end up with a reasonable quantitative estimate. On the other hand, recent work of the supervisor and collaborators has resulted in a new generation of the ground level sum-product estimates, which have not yet made their impact on growth in groups. The project will aim at doing this. On the initial stage it will focus on the affine group and SL2 over a field with positive characteristic, then attempt to build up on this towards more general group types.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1943257 Studentship EP/N509619/1 18/09/2017 31/03/2021 James Wheeler