From June - August 2016 I worked as a research intern under the supervision of Dr. Matt Roberts. This was a part of the summer research internship scheme run by the Bath IMI.

The purpose of this project was to use modern techniques, specifically spine decompositions, to prove some interesting results about a particular branching process. We started by proving the much older Kesten-Stigum theorem for Galton-Watson Branching Processes via these methods. This is a result which gives a set of equivalent characterisations of the asymptotic growth of a galton-watson population. Using the same spine techniques as used for the proof of the Kesten-Stigum theorem, we proved a similar result for the asymptotic growth of a specific branching random walk; specifically that the logarithm of the maximal displacement has almost-surely linear growth.

For more information about IMI internships, click here.

To read my paper, click here.

After finishing my MMath, I secured a second IMI internship working jointly with Dr. Chris Guiver from the department of Mathematical Sciences and Prof. Andrew Plummer from the department of Mechanical Engineering.