Currently I am a lead mathematical modeller working at Jacobs Engineering Group.
I work as a consultant on problems related to environmental science and disposal of radioactive waste, i.e. modelling hydrogeological systems and attempting to quanitfy uncertainties over very long time scales.
Before that I was a postdoctoral researcher in the Predictability of Weather & Climate group at Oxford University.
And before that I completed a PhD in pure maths, specializing in geometric analysis & partial differential equations.
Paxton, E A: Embeddedness of timelike maximal surfaces in (1+2)-Minkowski space, Annales Henri Poincaré (2020) 21 3035–3068 (journal | arXiv)
Paxton, E A; Chantry, M; Klöwer, M; Saffin, L; Palmer, T: Climate Modelling in Low Precision: Effects of Both Deterministic and Stochastic Rounding, Journal of Climate (2022) 35(4) 1215–1229 ( journal)
Kimpson, T; Paxton, E A; Chantry, M; Palmer, T: Climate-change modelling at reduced floating-point precision with stochastic rounding, Quarterly Journal of the Royal Meteorological Society; (2023) 149(752) (journal)
Klöwer, M; Coveney, P V; Paxton, E A; Palmer, T: Periodic orbits in chaotic systems simulated at low precision, Nature Scientific Reports; (2023) 13(1) (journal)
Paxton, E A; Wu, J; Hicks, T; Doudou, S; Applegate, D; Mason, R; Payne, L: GMIT: A tool to support post-closure criticality safety assessments, Proceedings of the 12th International Conference on Nuclear Criticality Safety; (2023) (journal article to appear soon)
Initial Value and Initial-boundary Value Problems for Timelike Maximal Surfaces in (1+2)-Minkowski Space (pdf):
My PhD thesis, written at Oxford in 2019. Chapter 1 is an introduction to the field, Chapters 2-4 are results on the initial-value problem for TMSs, while Chapters 5 & 6 contain work on the initial-boundary value problem for TMSs. Chapter 7 discusses some interesting open problems in the field.
Scattering and blow-up for semi-linear wave equations (pdf):
Written in summer 2016, under the supervision of Luc Nguyen while trying to learn about wave equations. Mostly a compilation of quite well-known results on scattering vs finite-time singularity for semi-linear wave equations, but the presentation is unique and a few proofs & heuristics are my own. I hope it gives a good survey for anyone interested in the topic :)
Compactness results for flowing to a harmonic map (pdf):
Written in spring 2016, under the supervision of Melanie Rupflin. It gives a brief introduction to harmonic maps from surfaces, focussing on the phenomenon of "bubbling". There are some pretty pictures to illustrate bubbling, and we also proved a new compactness result for maps from degenerating Riemann surfaces, which is written up in Section 3.
Exotic Spheres (pdf):
My Masters thesis, written at UCL in 2014/15, under the supervision of Jonny Evans. The goal was to give an exposition of John Milnor's famous construction of 7 dimensional "exotic spheres" (given in Section 4), and along the way we came up across a number of wonderful topics in differential topology such as fibre bundles, de Rham cohomology, cobordism, and characteristic classes.
Here is a 3D representation of the Lorenz attractor. This came from playing around with the threejs package, and being generally curious as to ways to represent a probability distribution in 3D. This one cuts 3D space into cubes (i.e. bins for a histogram) and represents probability mass by transparency.
"Embeddedness of Timelike Maximal Surfaces in (1+2)-Minkowski space". Slides:
(without clicks).
2020 Discussion Meeting on Zero Mean Curvature Surfaces---International Centre for Theoretical Sciences, July 2020.
"What is... The Wasserstein Distance".
Slides: (without clicks | with clicks)
Predictability of Weather and Climate group seminar---Oxford University, November 2020.