My work has generally focused on topics related to string theory and supergravity.
In particular I have worked on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. This is an equivalence (duality) of superstring theory and M-theory formulated on a product space of (d+1)-dimensional anti-de Sitter spacetimes with some compact Einstein manifold such as a sphere and certain superconformal field theories that live on d-dimensional Minkowskian spacetimes that correspond to the boundaries of the anti-de Sitter space. One remarkable fact about the AdS/CFT duality is that it relates a theory of gravity, such as string theory, to a theory with no gravity at all. It also relates highly non-perturbative problems in a super Yang-Mills theory, that may appear intractable, to problems in weakly coupled classical superstring theories or in supergravity, that may stand a chance of a solution. In the past we have studied the positive energy unitary irreducible representations of supergroups that are the symmetry groups of the AdS supergravity and the dual superconformal theory in various dimensions.
More recently we have studied the symmetry algebras of higher spin field theories. We have particularly explored the link between the minimal unitary representations and their deformations of the AdS symmetry algebras SO(d,2) and the massless conformal fields in d-dimensional Minkowskian spacetimes. Higher spin theories have attracted a lot of attention lately since they provide much more simple models of the AdS/CFT correspondence.