Mathematical Sciences: Symplectic Geometry: Moduli Spaces and Manifold Invariants

9403567 Weitsman The research entails the symplectic geometry of moduli spaces associated with Riemann surfaces. The focus will be on the use of methods from the the theory of toric varieties to study moduli spaces of vector bundles and certain conjectures concerning the moduli of curves. It is also planned to study the relation between the symplectic geometry of the moduli space of vector bundles and certain 3-manifold invariants. The research has potential applications to other areas of mathematics and also to quantum gravity and string theory in mathematical physics. ***