Research Interests: Homotopy theory, algebraic topology, derived algebraic geometry.
- Homotopy Harnessing Higher Structures, INI, various dates July-December 2018.
- Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects, Imperial College, 9-13 July 2018 .
- YaMCATS, University of Leeds, 16th July 2018.
- Accessible categories and their connections, University of Leeds, 17-20 July 2018.
- Galway Topology Colloquium, University of Birmingham, 23-25 July 2018.
- Crossed simplicial group categorical nerves - Applied Categorical Structures (2017).
- Homotopy of planar Lie group equivariant presheaves - Journal of Homotopy and Related Structures (2017).
- Computations for Symbolic Substitutions (with Dan Rust) - Journal of Integer Sequences (2017).
- Bousfield localisation and colocalisation of one-dimensional model structures (with Richard Garner) - (2018).
- Adelic models of Quillen model categories (with John Greenlees).
- Periodic points of the random period doubling substitution (with Dan Rust).
- A handbook of model categories.
Mathematics computer applications (written in Swift):
- Elliptic curves over finite fields - This is a small OSX application that allows you to work with elliptic curves over finite fields. The entry of the data is inuitive, however there are some "hidden" features. Clicking on a point and using the "zoom" gesture will show multiples of that point. Clicking and dragging a point to another point will add the points. While having two points added, doing the "zoom" gesture will show the lines used to calculate the addition.