Until May 2021, I was a DPhil student under Professor Christina Goldschmidt, who is based at the University of Oxford’s Department of Statistics and in the Oxford Probability group. My thesis, entitled The critical mean-field random cluster model, was based on work from the second year onwards of my doctoral studies. I had my viva in April 2021, which I passed with minor corrections. The corrected thesis appears below.

In my first year I investigated random planar graphs and random maps; details of this work will hopefully appear here at some point.

As an MMath student, also at the University of Oxford, I completed a thesis expounding existing results from the literature about explorations of random graphs, with a small amount of original work simulating random graphs. That thesis also appears below, but please note that it has not been corrected post-examination! (If you spot any errors I’d be interested to hear about them.)