• Algebraic groups play a role in several parts of mathematics. I am particularly interested in simple algebraic groups over algebraically closed fields. These were classified by Chevalley in the 1950s, and are just the simple Lie groups over the appropriate fields. One of my main interests is the problem of determining the subgroup structure of these groups. Currently I am working on several problems in this area, the two main ones being

(1) to determine the maximal closed subgroups of the simple algebraic groups of exceptional types, and

(2) to determine and study those pairs X,Y of closed subgroups of a simple algebraic group G, such that there are only finitely many (X,Y)-double cosets in G.