I’ve written a 15 page introduction to topology as part of my MSc in Pure Mathematics at the University of Manchester. The task was to write a 12-16 page report on an undergraduate level topic as practice for the summer dissertation. Since I was already comfortable writing Latex but have never had the opportunity to attend a taught course on topology, this seemed like a good opportunity to fill in some gaps for myself: download pdf.

I wrote my Cambridge Part III thesis on statistical sampling using Markov Chain methods under Dr Will Handley. Unfortunately I broke both my right wrist and left index finger at the beginning of the second semester - due to university views on mitigation my department refused extensions or accommodations and I was left to complete the work without supervisor input.

I am still working to investigate some of the observations I noted. I am particularly interested in the resonance behaviour observed in my labbook on 2025/02/20 - periodic solutions to the Hamiltonian can introduce a “beating” effect and lead to poor mixing.

The partial submission I was able to make whilst still injured can be found here as well as my intial first semester initial progress report.

Summer UROP 2024 modelling collective cell motion in biological tissues: download pdf