Mathematical Sciences: The Topology of Algebraic Varieties

将学习代数簇的拓扑学的各个方面。重点将放在新的拓扑不变量或技术的发展上(例如交同调、模上同调、反曲)，以及对在应用中重要的特定变种的研究(例如模变元、配置空间)。代数簇是由多项式方程定义的空间。它们应该特别简单，但它们的拓扑结构可能比这更复杂。由于它们出现在许多不同的背景下，因此对它们进行分类和分析是很重要的。

Aspects of the topology of algebraic varieties will be studied. Particular emphasis will be on the development of new topological invariants or techniques (e.g. Intersection Homology, Motivic Cohomology, Perverse Sheaves) and on the study of particular varieties which are important in applications (e.g. Modular Varieties, Configuration Spaces). Algebraic varieties are spaces defined by polynomial equations. They should be particularly simple, but their topology can be more complicated than this suggests. Since they arise in many different contexts, it is important to classify and analyze them.