Ben graduated with the MMath Mathematics from Bath in 2025, focusing on probability and analysis.  His final year project was on branching processes, trying to prove some results concerning the asymptotics of the branching random walk. His research interests are random graphs, percolation, branching processes and related models. Ben also completed a summer research project with Antal Járai on the Abelian Sandpile model. 

Outside of maths, Ben is a big fan of language learning, poker, cooking (proper) carbonara and Formula 1.  

Project title:
Extending planar scaling relations and steepness of the percolation probability to slabs.

Supervisor(s):
Christoforos Panagiotis, Antal Járai

Project description:
Percolation is one of the simplest models of random graphs which exhibits a phase transition, associated to this phase transition we have several quantities called critical exponents which describe the critical (the tipping point of the phase transition) behaviour of the model. In the planar setting, it is relatively straightforward to prove relations between these quantities (if one assumes they exist). It is believed that slabs lie in the same universality class as planar percolation models, thus one would expect these scaling relations to hold, as well as other related properties.

My project aims to prove some results of this type.