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, 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.
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 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. 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.
From July 17 to 20 I hosted a workshop on accessible categories and their connections - see the workshop webpage.
There is a fairly up-to-date list of my publications on my standard School of Mathematics webpage. They are reviewed on MathSciNet (subscription required), and here are the papers themselves on the arXiv.