Mathematical Sciences: Symplectic Geometry: Moduli Spaces and Manifold Invariants

[403567] Weitsman研究涉及与黎曼曲面相关的模空间的辛几何。重点是利用环变理论的方法来研究向量束的模空间和关于曲线模的一些猜想。研究了向量束模空间的辛几何与某些3流形不变量的关系。该研究对数学的其他领域以及数学物理中的量子引力和弦理论具有潜在的应用前景。＊＊＊

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. ***