In the course of their research, members of the Department of Pure Mathematics touch on problems related to physics, including operator algebras, path integrals, quantization and nonlinear PDEs.

Hendrik Grundling works on mathematical physics problems in the two areas of quantum field theory and quantization theory. In quantum field theory he is concerned with issues arising from gauge theory and in particular the problem of quantum constraints. The analysis is done in the context of operator algebras, so he is also concerned with problems in that area as well as with the representations and actions of groups which are not locally compact. In quantization theory, he studies the existence and uniqueness of quantizations of Poisson algebras associated with simple manifolds other than the plane.

Brian Jefferies is interested in the mathematics of path integrals and their connection with stochastic equations and measure theory. As well as their pervasive use in quantum physics, path integrals in the guise of a heuristic calculational tool are appearing in ever-increasing areas of mathematics, such as knot theory and low dimensional topology. He is the author of "Evolution Processes and the Feynman-Kac Formula", published by Kluwer in 1996. His interests overlap with the harmonic analysis and functional analysis groups.

John Steele's interests are in the area of General Relativity, particularly in exact solutions of the Einstein Field Equations, their symmetries and interpretation. He is also interested in geometric aspects of mathematical physics and the history of mathematical physics.

Norman Wildberger is interested in Lie group representation theory and the connections with quantization procedures, specifically geometric quantization, star products and Kirillov theory. Another interest is that of commutative hypergroups, of which the fusion rule algebras from conformal field theories provide rich examples, and connections with duality. Lately he has been very interested in combinatorial constructions of Lie algebra representations, trying to obtain explicit models of for example sl(3) modules (the symmetry algebra of the strong force) which are easier to implement than Gelfand Tsetlin. He is especially interested in extending these and related ideas coming from games on graphs to obtain modules for general Kac Moody algebras.

Patrick Costello is working with Hendrik Grundling.