Hello!
I am a PhD student under the supervision of Prof. Jamie Vicary at the Department of Computer Science and Technology, University of Cambridge. I am a member of the Cambridge Logical Structures Hub (CLASH).
My research is about higher categories as algebraic and directed notions of space, and the main problem I am working on is understanding the homotopy theory of weak omega-categories. I am interested in approaching these problems with computational methods and ideas from dependent type theories, such as Homotopy Type Theory (HoTT) and CaTT, as well as diagrammatic calculi.
More broadly, I am interested in internal languages of higher structures. Just as higher-order logic is the internal language of an elementary topos, HoTT can be interpreted in every ∞-topos, so that type theory becomes a synthetic language for reasoning inside these universes of spaces. I am working on understanding what the corresponding languages look like for directed and higher-dimensional structures.
Interests
- Higher Category Theory
- Homotopy Type Theory
- Globular Methods
- Type Theory
- Proof Assistants
- Internal Languages
- Topos Theory
Research Projects
Selected Talks
- Posetal diagrams, ACT conference, Maryland (remote) Aug 2023
- Posetal diagrams, YAMCATS seminar, Leeds Jun 2023
- Posetal diagrams, POODLE seminar, Oxford Jun 2023
- On some impossible properties of the affine line object, Part III seminar, Cambridge Apr 2022
Notes
- Quantum Field Theory, read by Prof. N. Dorey, Michaelmas 2022
- Coxeter Groups, read by Dr. R. Boyd, Lent 2022
- Infinite Groups, read by Dr. H. Bradford, Lent 2022
- Large Cardinals, read by Prof. B. Loewe, Lent 2022