About

I'm a third year DPhil student at the University of Oxford with a doctoral scholarship from the Alan Turing Institute. I work in applied topology and am jointly supervised by Vidit Nanda and Ulrike Tillmann. I completed my MMath at the University of Warwick, graduating in 2017. My MMath dissertation was supervised by David Mond. Prior to starting my PhD, I worked as a software developer (C#) at Bank of America Merrill Lynch.

Research

I'm a member of the Topology and Data Science research groups and I'm part of the Centre for Topological Data Analysis. My main interests are computational algebraic topology, computational neuroscience, network analysis and applied knot theory.

During my DPhil I've taken graduate courses in Homological Algebra, Category Theory, Differentiable Manifolds, Probability & Statistics for Network Analysis and Machine Learning.

A generalised clock theorem

Joint with Daniele Celoria

We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function on the 2-sphere and simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson’s correspondence.

Filtered matchings and simplicial complexes

Joint with Daniele Celoria

We associate to any simplicial complex a filtration, starting from the discrete Morse complex and finishing at the matching complex. We define some homology theories and provide computations to help to understand these complex objects.

Topological comparison of graph metrics

Joint with Ana Garcia-Pulido, Kathryn Hess, Jane Tan, Katharine Turner & Bei Wang

Motivated by modelling the brain as a digraph, we investigate whether standard digraph metrics capture topological information about the associated directed flag complex, for various random digraph models. (In preparation.)

Teaching

I am a Tutor at St Catherine's College, Oxford for the following courses:

  • Introduction to Calculus (2021)
  • Probability (2020–21)
  • Introduction to University Maths (2020)
  • Statistics & Data Analysis (2020)
  • Groups & Group Actions (2019)
  • Analysis I, II and III (2018–19)
  • Linear Algebra I and II (2018–19)

I've been a Teaching Assistant for:

  • Topology & Groups (2020)
  • Category Theory (2018)

I've created some Jupyter notebooks for the Probability and Statistics for Network Analysis course, which implement and explain some of the course content.