51福利

Research Overview

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.

PhD Supervision Interests

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.