Mathematical Sciences: Cycles, Residues & Global Problems in Geometry

9505174劳森提出的研究是代数几何和代数拓扑的交叉。一个主要的目标是进一步发展关于射影变的代数循环理论：这个理论，主要是由劳森创立的，试图从拓扑的角度来理解射影变，并且可以被认为是方案理论的推广。将代数变量定义为若干变量的齐次多项式集合的公共零集；代数几何是研究代数变量（或者同样的，在几个复杂变量中的齐次多项式方程）的学科。提出的研究涉及应用拓扑工具来研究代数变体的各种子集。

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.