I'm broadly interested in category theory and its applications to computer science, logic, probability theory, systems design, and more.
We establish connections between conditional probability in Markov categories and Beck-Chevalley monads and give a universal characterization of 'hypernormalization'.
Exploration of the relationship between conditional probability in Markov categories and Beck-Chevalley monads.
Presentation of our recent work connecting category theory and probability theory.
We explore how one can model concurrent processes using string diagrams. We also introduce the 'conductor' as a way to synchronize otherwise asynchronous Petri places.
We study how one can use discrete Morse theory to speed up the computation of persistent homology of sequences of cosheaves on a finite simplicial complex. This mini project is now part of Oxford's Past Papers Archive.
Shows how one can use the Leray-Serre spectral sequence to compute the homotopy groups of spheres mod torsion.