ProfessorThe Department of Mathematics and Statistics
Burnside Hall, Room 1109
805 Sherbrooke W.
H3A 0B9, Canada
Phone: (514) 398-3816
Fax: (514) 398-3899
1. Topology of moduli spaces (in collaboration with Charles Boyer (UNM) and Jim Milgram (Stanford)): The question is to find out how moduli spaces of instantons or of holomorphic curves behave as one stabilises with respect to charge or degree. One generally shows that topological invariants of these spaces then stabilise.
2. Geometry of integrable systems (in collaboration with John Harnad (CRM) and Eyal Markman (U. Mass.) ): Geometric constructions of integrable systems, their solution, their classification.
3. Moduli spaces on Riemann surfaces. (in collaboration with Lisa Jeffrey (Toronto)): There is a correspondence, due to Narasimhan and Seshadri, which links representations of the fundamental group of a Riemann surface into the unitary groups to holomorphic vector bundles on the surface. The project is concerned with certain generalisations of this correspondence.