I am a University Academic Fellow in the School of Mathematics of the University of Leeds. I also hold an EPSRC Early Career Fellowship, with the research project Bringing set theory and algebraic topology together.
I currently have 3 doctoral students, Stamatis Dimopoulos, graduating in 2018, John Howe (co-supervised with John Truss), and Richard Matthews (co-supervised with Michael Rathjen).
I mainly work in set theory, and am especially interested in large cardinal axioms. These posit the existence of cardinals (infinities) so large that they cannot be proven to exist from the standard axioms for mathematics. By assuming that they do exist, we strengthen the theory, and so are able to draw more conclusions and do more mathematics than we could otherise.
A big feature of my research is applictions of set theory to other areas of mathematics, particularly category theory and algebraic topology. Indeed, this is the topic of my EPSRC Early Career Fellowship.
This page is still a work in progress. For the time being, here are my publications reviewed on MathSciNet (subscription required), and here are the papers themselves on the arXiv. I also have a spartan, incomplete standard School of Mathematics webpage.