The best way to think of a group is the abstraction of the idea of symmetry. A Lie group is a group that is also continuous in a compatible way; think of the symmetry of a circle. Lie algebras can be thought of as an 'infinitesimal' approximation to Lie groups.  One can think of representation theory as taking algebraic objects and 'representing' them as matrices acting on a vector space. There is a beautiful classification of particular Lie algebras by root systems. All of the algebraic objects I study also have these root systems. For example, Weyl groups, Coxeter groups, Lie groups, Lie algebras, Hecke algebras, Cherednik algebras, Brauer algebras, Grassmanians. 

I am particularly interested in variants of Schur-Weyl duality and diagram algebras, as well as Howe duality - linking two Lie algebras or similar. 

I am also interested in Grassmanians, particularly outside of type A. From a cohomological and tropical perspective. 

I am happy to take on PhD students and have the following potential projects. Schur-Weyl duality and variants for Spin groups, Deformed Howe Duality, Cohomology of Grassmannians, Clifford algebras and exterior algebras of Lie algebra pairs.

I am a Lecturer in the Department of Mathematics and Statistics. My research interests are algebraic representation theory, more specifically Lie groups, Lie algebras, Grasmmannians, De Rham cohomology, Schur-Weyl and Howe duality. 

Personal webpage: https://www.maths.lancs.ac.uk/~calvertk/