Adam Paxton's Page

E. Adam Paxton

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About me

I am a postdoctoral researcher in the Predictability of Weather & Climate group at Oxford University. Before this I completed a PhD in pure maths, specializing in geometric analysis & partial differential equations.

Publications

Embeddedness of timelike maximal surfaces in (1+2)-Minkowski space (arXiv, Annales Henri Poincaré (2020) 21:3035-3068 )

Notes

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.

Talks

Conferences

"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.

Seminars

"What is... The Wasserstein Distance". Slides: (without clicks | with clicks)
Predictability of Weather and Climate group seminar---Oxford University, November 2020.

Photos

The shots at the top are from Oxfordshire, Ladakh, Breccon Beacons, Senegal, and Lahore. More photos may follow at some point :)