Mathematical Sciences: Algebraic Topology of Algebraic Varieties; Conformal Field Theory

代数变种的拓扑方面，密切相关的算术性质，将被研究。特别强调的将是新的拓扑不变量的发展（例如各种版本的动机反常轴），以及在共形场论中出现的结构（环空间的几何）。这项工作结合了理论物理学和几何学的思想，使用的方法同样多样化。

Aspects of topology of algebraic varieties, closely related with their arithmetic properties, will be studied. Particular emphasis will be on development of new topological invariants (e.g. various versions of motivic perverse sheafs), and on structures emerging in conformal field theories (geometry of loop spaces). This work combines ideas from theoretical physics with others from geometry, using methods which are equally diverse.