Paul Leask


Paul is a mathematical physicist specialising in the areas of differential geometry, topology and elementary particle physics. He is currently a second year PhD student at the University of Leeds and a member of the geometry group. His research project is the quantisation of Skyrmions stabilised by vector mesons. Paul graduated from the University of Glasgow in 2019, with Honours of the First Class. While there, he read mathematics & physics with a focus on topological solitons in gauge field theories.

Research interests

The Skyrme model is a nonlinear field theory of pions that possesses topological solitons that describe baryons. It has been derived as a low-energy effective field theory of quantum chromodynamics (QCD) in the large colour limit and, more recently, from holographic QCD models such as the Sakai-Sugimoto model. One of the outstanding problems in the Skyrme model is the correct prediction of nuclear binding energies, which one would like to be able to predict using the Bethe-Weizsacker semi empirical mass formula. The classical mass of a Skyrmion roughly plays the same role as the volume and surface terms. So, to be able to address these first two terms, we need to understand the phases of nuclear matter in the Skyrme model. As the ground state of nuclear matter has a crystalline structure in the classical approximation, understanding the infinite crystalline structure is key. The majority of Paul’s research so far has been determining this infinite crystal structure in the Skyrme model (and baby Skyrme model) by varying over all possible lattices.


  • MSci Mathematics & Physics

Research groups and institutes

  • Geometry