Research

I am a mathematician in the School of Mathematics at the University of Bristol.  By day I research extremal combinatorics, and by night I talk maths at anyone who will listen.

I have an annotated bibliography of my papers, and an open notebook of things I’ve learnt and don’t want to forget.

Research interests

Extremal combinatorics

Understanding large discrete objects is both increasingly important in practice and computationally difficult.  Extremal combinatorics seeks to answer questions of the form “how large/small can a discrete structure be so that a given property does/does not hold?”  By probing the extreme cases of difficult problems we can learn about their structure, for example by discovering simpler necessary or sufficient conditions for properties to hold.

Ramsey theory

In any group of six people, either some three people all know each other or there are some three people none of whom know either of the others.  This is the beginning of Ramsey theory, the study of unavoidable patterns in large unstructured objects.  The patterns I look for are infinite, and the tools used to find them are surprising; many results rely on “ultrafilters”, objects which are known to exist but are impossible to specify precisely.