Dr Ben Lees
My research mainly concerns models of statistical mechanics such as spin systems and their graphical representations, discrete models from probability, and quantum information. These models are motivated from physics and probability and have applications to topics such as phase transitions, condensed matter, and quantum mechanics.
Many beautiful models of spin interactions have a graphical representation in terms of one-dimension objects (loops, walks,...) living on a higher dimensional space. Many of these objects may exist simultaneously (a loop soup) and they interact according to certain rules that can be derived from the original spin models. By understanding these models using techniques from probability we can learn about the physical models and their properties. For example, magnetism in a spin model may correspond to the existence of long loops in the graphical representation, or an external field (magnetic, electric...) could manifest itself in the graphical model as a “sink” vertex that “kills” loops that visit it.
More recently I have become interested in correspondences between models such as the Asymmetric Simple Exclusion Process and Zero Range Process or between the Ising model and interactions particles systems and how these correspondences lead to identities between integer partion identities of interest to number theory.
I am very happy to supervise Masters and PhD projects in these areas. Please contact me for further information.<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>
- PhD Mathematics, University of Warwick 2016
<li><a href="//phd.leeds.ac.uk/project/1881-combinatorial-identities-from-interacting-particle-systems">Combinatorial identities from interacting particle systems</a></li>