Stewart

David Stewart

My research interests are in Algebra. Specifically, algebraic groups: subgroup structure, modular representation theory, non-abelian cohomology.

I am working towards a classification of all Zariski closed, connected, reductive subgroups of the exceptional algebraic groups, i.e. those with root systems G_2, F_4, E_6, E_7 or E_8. The question become interesting where the groups are defined over fields of positive characteristic, due partly to the existence of (following Serre) 'non-G-cr' subgroups. Finding these involves calculations of non-abelian cohomology of groups with coefficients in unipotent groups (i.e. p-groups).

I am also investigating the extent to which one can bound the dimensions of usual (Hochschild) cohomology groups of algebraic groups with coefficients in simple modules, related to a conjecture of Guralnick: there is a universal bound on the dimension of H^1(G,L) where G is any finite simple group and L is any absolutely irreducible representation for G. (The highest known is currently 3.)

Website at Mathematical Institute

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Email: david.stewart@new.ox.ac.uk