Dr David I. Stewart
Dr David I. StewartPhD, BA, MA, CASM, PGCE (Post-compulsory)
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.)
G-complete reducibility and the exceptional algebraic groups (PhD Thesis, Imperial College; supervisor: Martin W. Liebeck)
Unbounding Ext, J. Algebra 165 (2012) 1-11.
The second cohomology of simple SL2-modules, Proc. Amer. Math. Soc., 138, 427--434 (2010)
The second cohomology of simple SL3-modules, Comm. Alg. (to appear)
Restriction maps on 1-cohomology of (algebraic) groups, (submitted)
The reductive subgroups of G2, J. Group Theory, 13, 117--130 (2010)
The reductive subgroups of F4, Mem. Amer. Math. Soc., (to appear)
Non-G-completely reducible subgroups of the exceptional groups, submitted.
(with B. Parshall and L. Scott) Shifted generic cohomology, submitted.
(with C. Bendel, D. Nakano, B. Parshall, C. Pillen and L. Scott) Bounding extensions for finite groups and Frobenius kernels, submitted.
Recent Publications (from MathSciNet):
Representation Theory 2a, class.
Group Theory 2b, class.
This page is maintained by . Please use the contact form for feedback and comments.