+44 1865 615104
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Broadly, I like learning about mathematical physics, general relativity, differential geometry and PDEs. My main research focus currently is timelike surfaces with prescribed mean curvature in Lorentzian geometry.
For a link to my work on timelike maximal surfaces and some notes, go to my webpage http://people.maths.ox.ac.uk/paxton/
Prizes, awards, and scholarships:
My doctoral studies are supported by EPSRC grant [EP/L015811/1].
Major / recent publications:
Embeddedness of timelike maximal surfaces in (1+2) Minkowski space. Submitted. https://arxiv.org/abs/1902.08952
^^^Above is my first paper on timelike maximal surfaces, any comments would be very welcome!
Below are a few reports that I have written whilst a graduate student. Now of course I see all kinds of ways they could have been written better, and largely there is nothing which can't be found done better in textbooks. Nonetheless I'm putting them up online in case they may be of use to someone :)
Scattering & blow-up results for semi-linear wave equations: http://people.maths.ox.ac.uk/paxton/Waves
^^^ I wrote this in summer 2016, under the supervision of Luc Nguyen, whilst trying to learn about wave equations. Its mostly a compilation of well-known results on scattering of waves which can be found treated much more comprehensively in books.
Compactness results for flowing to a harmonic map: http://people.maths.ox.ac.uk/paxton/HarmonicMaps
^^^ I wrote this in spring 2016, under the supervision of Melanie Rupflin, on harmonic maps. It gives a brief introduction to harmonic maps from surfaces, focussing particularly on the phenomenon of "bubbling".
The de Rham Cohomology, Cobordism & Characteristic Classes: http://people.maths.ox.ac.uk/paxton/ExoticSpheres
^^^ This is my masters thesis, written at UCL in 2014/15, under the supervision of Jonny Evans. The main goal was to give an exposition of John Milnor's famous construction of 7 dimensional "exotic spheres".