I have been interested for many years in the subgroup structure of the Classical Groups, both finite and infinite. In particular I am interested determining classes of subgroups that are maximal as subgroups, both describing the subgroups in terms of geometric configurations and proving maximality using natural geometric techniques. I am also interested classes of almost simple subgroups that can be described geometrically, even if they are not maximal.
I am interested in certain geometric configurations. Sometimes, but not always, these are related to subgroups of Classical groups. The configurations that I have a particular interest are: caps in projective spaces; ovoids and partial ovoids in polar spaces; special sets on hermitian surfaces; blocking sets on hermitian surfaces.
SFY0001 (Basic Mathematics)
MAS1043 (Optimisation and Linear Methods)