Dr David I. Stewart
 Dr David I. StewartPhD, BA, MA, CASM, PGCE (Post-compulsory)
eMail:
David [dot] Stewart [-at-] maths [dot] ox [dot] ac [dot] uk CV: cv.pdf Phone Number(s):
Reception/Secretary: +44 1865 273525 Office: SGT4 Departmental Address:
Mathematical Institute |
Research Interests:
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.) Major/Recent Publications:
G-complete reducibility and the exceptional algebraic groups (PhD Thesis, Imperial College; supervisor: Martin W. Liebeck) Unbounding Ext, J. Algebra (revised and resubmitted) 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) Recent Publications (from MathSciNet):
Teaching:
Representation Theory 2a, class. Group Theory 2b, class. Further Details:
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