Cardiff Mathematics Independent Website
Welcome to my personal research homepage. Most of my work focuses on the rigorous algebraic underpinnings of two dimensional conformal field theory, and, more recently, integrability and its connections to the Yang-Baxter equation.
The algebraic axiomatisation of the symmetries underlying a two dimensional conformal field theory is called a vertex (operator) algebra. Vertex algebras can be thought of as a kind of generalisation of associative commutative but different from associative non-commutative algebras. As with associative algebras, much can be learnt from studying modules and many questions in the study of conformal field theory boil down question in vertex algebra module theory.
The most studied vertex algebras are the so called rational vertex algebras. These are distinguished by the fact that their module categories are semisimple with only a finite number of isomorphism classes of simple modules. I focus on vertex algebras for which neither the semi-simplicity nor the finite number of simple modules assumption need hold. Vertex algebras for which the semi-simplicity assumption fails are called logarithmic vertex algebras and the conformal field theories associated to them are ca
Cardiff Mathematics Independent Website