Mathematical Sciences: Gaussian Maps and Topology of SurfaceSingularities

这项研究是在代数几何中进行的，专门研究曲面奇点的不变量和变形。主要研究人员将研究曲面奇点链拓扑中的两个问题：一个涉及同调三维球面的Casson不变量，另一个涉及主要研究人员对射影曲面的Miyaoka不等式所做的工作中产生的一个神秘的新不变量。他还将研究一个由曲面奇点引起的问题，即研究曲线和均匀空间的“高斯映射”。本研究的主题是代数曲面及其奇点的拓扑。某些数字不变量被附加到这些对象上，这有助于对它们进行分类。首席研究员将研究这些不变量。

This research is in algebraic geometry, specifically studying invariants and deformations of surface singularities. The principal investigator will study two problems in the topology of links of surface singularities; one involves Casson's invariant of a homology 3-sphere, the other involves a mysterious new invariant arising from the principal investigator's work on Miyaoka's inequality for projective surfaces. He will also study a problem arising from surface singularities, the study of "Gaussian maps" for curves and homogeneous spaces. The subject of this research is the topology of algebraic surfaces and their singularities. Certain numerical invariants are attached to these objects which help in classifying them. The principal investigator will study these invariants.