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

代数簇的拓扑方面，密切相关 与他们的算术属性，将被研究。 特别 重点将放在发展新的拓扑不变量 (e.g.各种版本的动机反常sheafs），等等 在共形场论中出现的结构（环的几何 空格）。 这项工作结合了理论物理学的思想， 另一些来自几何学，使用同样不同的方法。

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.