I am a University Academic Fellow in the School of Mathematics of the University of Leeds. Until recently I also held an EPSRC Early Career Fellowship, with the research project Bringing set theory and algebraic topology together.
I currently have 3 doctoral students, John Howe (co-supervised with John Truss), Richard Matthews (co-supervised with Michael Rathjen), and Bea Adam-Day (co-supervised with Dugald Macpherson). My former student Stamatis Dimopoulos graduated in 2018.
The short, sweet, layman's summary of my research is that I study infinity. There's an excellent introductory video on YouTube made by Vsauce that starts very basic but goes pretty deeply into the concepts involved.
In more technical detail, 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 (assumptions) for mathematics. By assuming that such large cardinals do exist, we strengthen the theory, and so are able to draw more conclusions and do more mathematics than we could otherwise.
A big feature of my research is applictions of set theory to other areas of mathematics, particularly category theory and algebraic topology. Indeed, this was the topic of my EPSRC Early Career Fellowship. I have also started to pursue connections with abstract model theory, as the same parts of category theory as arise in my previous work turn out to be relevant in that context as well.
Probably the best source for my papers is my arXiv author page. They are reviewed on my author page at MathSciNet (subscription required), and there is a fairly up-to-date list of them with links to the published, journal versions at the bottom of my standard School of Mathematics webpage.