School of Mathematics

Prof Paul P Martin

Professor of Pure Mathematics
Head of Pure Mathematics

Contact details

Room: 9.18n
Tel: +44 (0)113 3437787
Email: P.P.Martin @ leeds.ac.uk

Keywords

Representation theory
Diagram categories and algebras
Statistical Mechanics

Research interests

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.

Modeling as an approach to understanding is not limited to physics. One can attempt to model abstract structures (such as groups of symmetries) by modeling. 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 modeling 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 modeling 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 modeling.

See the links on my personal homepage for many more details.

Useful links

personal home page

Postgraduate students

Chwas Ahmed (2012)
Heather Burke (2009)
Mufida Hmaida (2013)
Ahmed Hussein (2012)
Andrew Reeves (2008)

Selected publications

M. Alvarez and P. P. Martin. Higher-dimensional Temperley-Lieb algebras J Phys A 40 (2007) F895-F909.

A. Cox, M. De Visscher and P. P. Martin. The blocks of the Brauer algebra in characteristic zero Representation Theory 13 (2009), 272-308.

P. P. Martin. On diagram categories, representation theory and Statistical Mechanics AMS Contemporary Math 456 (2008) 99-136.

R. Marsh and P. P. Martin. Tiling bijections between paths and Brauer diagrams Journal of Algebraic Combinatorics, 33, no. 3 (2011), 427-453.