Professor Paul Martin
My research is concerned with the representation theory of structures (such as groups and algebras) used in physical modelling.
Physics can be thought of an attempt to understand, and make use of, the physical world. Part of the process of understanding any system is to make models of it. Such models can range from scaled-down versions, to mathematical simulations. My research is concerned with making useful mathematical models.
Modelling as an approach to understanding is not limited to physics. One can attempt to study abstract structures (such as groups of symmetries) by modelling. In this setting the process is called Representation Theory.
We often find ourselves in the situation that a mathematical model of a physical system is still rather complicated, and benefits from modelling itself. Thus one aspect of my research is concerned with the representation theory of structures which in turn model phenomena in physics (typically in Statistical Mechanics).
A wonderful feature of this modelling chain is that the non-abstract end system is amenable to other approaches, such as experiment and physical intuition. Thus not only does the representation theory inform the physics, but also the physics informs the representation theory. By pursuing this line, many exciting new pieces of mathematics have been discovered.
In summary then, my research is concerned with the representation theory of structures (such as groups and algebras) used in physical modelling.
See the links on my personal homepage for many more details.<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>
- Combinatorial Representation Theory: Algebra and its interfaces with geometry, topology and combinatorics
Research groups and institutes
- Pure Mathematics