Postgraduate Research Student
Email: email@example.comRoom Number: Mathematical Sciences Building, Room: MB-402
William’s main research interests are in combinatorics. Most of William’s work has been on problems in extremal combinatorics making use of probabilistic and algebraic methods. Problems in extremal combinatorics ask for the maximum possible value of a certain parameter of a combinatorial system, subject to given constraints.
William has contributed results in combinatorics that are naturally phrased in the language of representation theory, obtained some discrete isoperimetric inequalities and is currently completing work on an extension of the classical Erdos-Ko-Rado intersection theorem.
He is also interested in the application of Fourier analysis and other algebraic methods to combinatorial problems, and is keen to explore the use of spectral methods, the analysis of Boolean functions and representation theory on problems in extremal, probabilistic and additive combinatorics.
William is particularly fond of problems which are easily stated and understood, but which elude attack by standard arguments.
William is supervised by Dr David Ellis.
William's research statement can be found here:
- Smallest cyclically covering subspaces of F_q^n, and lower bounds in Isbell's conjecture, Eurpean Journal of Combinatorics, Volume 81, October 2019, pages 242 - 255, https://arxiv.org/abs/1810.03485.
- Edge Isoperimetric Inequalities for Powers of the Hypercube, submitted, https://arxiv.org/abs/1909.10435.