Nick’s thesis is titled ‘Bieri-Strebel Groups With Irrational Slopes’, and he considers a group of continuous piecewise-linear homeomorphisms of the unit interval for which every slope has gradient which is a power of some quadratic integer. Under the supervision of Professor Brita Nucinkis, Nick’s work aims to determine for which choices of quadratic integer we can represent every such homeomorphism as a tree-pair diagram.  

Nick has been able to successfully identify the conditions for these quadratic integers. For groups such that the quadratic integer satisfies these conditions, and hence tree-pair representation of each homeomorphism, Nick finds explicit presentations. These presentations are notable for containing only two families of generators and two families of relations.

The examiners were Professor James McKee of Royal Holloway University of London, and José Burillo of the Polytechnic University of Catalonia. 

Nick is now taking on a new challenge, becoming a RIS (researcher in school) trainee teacher of mathematics, a role which will include developing educational research and promoting access to higher education for students of all backgrounds. 

During his time at RHUL Nick was active in numerous outreach events. In particular he was instrumental in  RHUL’s part in the exhibition on GCHQ at the Science Museum in London. He participated  in many WISDOM events and was regularly seen at our research seminars. We wish Nick all the best for his future!