# Thomas Sales

I am a first year PhD student, supervised by Professor Charles Elliott. My research interests are in numerical/functional analysis, and PDEs.

I completed my MMath at the University of Bath, supervised by Dr Pranav Singh, where my project was about approximate conservation of energy by numerical integrators. In particular, it looked at exponential splitting methods for the time dependent Schrödinger equation. An example of this is the Lie-Trotter splitting

$e to the minus i h H u 0 is approximately e to the i h Laplacian e to the minus i h V u 0$.

A copy of this can be found here, complete with all the typos I submitted it with.

My project for this year is on 'Surface Finite Element Methods for the Cahn-Hilliard Equation with a logarithmic potential'.

Time evolution of the solution of the Cahn-Hilliard equation on a torus.

Photo of me (left) at my graduation.