Mathematical Sciences: Cycles, Residues & Global Problems in Geometry

9505174劳森，拟议的研究位于代数几何和代数拓扑的交界处。一个主要目标是进一步发展射影簇上的代数圈理论：这一理论主要由Lawson创立，试图从拓扑的角度理解射影簇，并可被视为方案理论的推广。代数族被定义为多个变量的齐次多项式的集合的公共零集；代数几何是研究代数族(或同样的，多个复变量的齐次多项式)的学科。所提出的研究涉及应用拓扑工具来研究代数簇的各种子集。

9505174 Lawson The proposed research lies at the interface of algebraic geometry and algebraic topology. A principal goal is to further develop the theory of algebraic cycles on projective varieties: this theory, largely founded by Lawson, seeks to understand projective varieties from a topological standpoint, and can be considered as a generalization of the theory of schemes. An algebraic variety is defined as the common zero set of a collection of homogeneous polynomials in several variables; algebraic geometry is the study of algebraic varieties (or what is the same, homogeneous polynomial equations in several complex variables). The proposed research has to do with applying topological tools to study various subsets of algebraic varieties.