Topology of Algebraic Varieties

该奖项将支持在西班牙萨拉戈萨大学举行的代数品种拓扑学会议。这次会议的主题源于20世纪初奥斯卡·扎里斯基的作品。随着低维拓扑学的不断进步，Zariski关于低维复数簇、它们的奇点和模数的原始问题今天仍然吸引着人们的兴趣。这次会议的主题包括辫子单线、基本群、Alexander不变量、局部系统、镜像对称性、环面几何、特征类和Hodge理论。多项式方程的解，从古希腊人研究的低次超曲面到今天用于弦理论和量子场论的模型，形成了丰富的对象类别。从拓扑的角度研究代数簇有两个原因：一方面，由代数结构施加的约束导致对拓扑的约束，另一方面，拓扑信息可以导致关于簇的模和奇点的性质的代数几何信息。代数簇的拓扑学涉及包括奇点理论和Hodge理论在内的广泛的研究课题。

This award will support a conference on the Topology of Algebraic Varieties at the University of Zaragoza in Spain. The subject of this conference grew out of Oscar Zariski's work from the early part of the 20th century. Zariski's original questions concerning low-dimensional complex varieties, their singularities, and moduli continue to hold interest today, as more light is shed on them by continued advances in low-dimensional topology. Topics included in this conference are braid monodromy, fundamental groups, Alexander invariants, local systems, mirror symmetry, toric geometry, characteristic classes and Hodge Theory.Solutions to polynomial equations, from low degree hypersurfaces studied by the ancient Greeks to models used in string theory and quantum field theory today, form a rich class of objects. Reasons to investigate algebraic varieties from a topological point of view are 2-fold: constraints imposed by the algebraic structure lead to constraints on topology on the one hand, and on the other hand topological information can lead to algebreo-geometric information about the moduli of varieties, and about the nature of singularities. The topology of algebraic varieties intersects a wide range of research topics including singularity theory and Hodge theory.