Mathematical Sciences: Geometry and Topology

调查员将对各种问题进行研究 与代数空间的拓扑性质有关。 他 打算研究代数簇的拓扑，特别是 平面代数曲线族的不变量 代数簇上的光滑结构，以及 无穷大附近的复多项式 将空间的代数结构与拓扑结构联系起来， 一些最基本和最重要的问题的来源 数学 它需要各种各样的技术， 挑战了拓扑学和代数学的主要人物， 国外

The investigator will pursue research on various questions concerned with topological properties of algebraic spaces. He intends to study the topology of algebraic varieties, especially invariants of families of plane algebraic curves, invariants of smooth structure on algebraic varieties, and the behavior of complex polynomials near infinity. Relating algebraic to topological structure of spaces is a source of some of the most basic and important questions in mathematics. It calls upon a wide variety of techniques and has challenged major figures in topology and algebra both here and abroad.