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

研究与代数簇的算术性质密切相关的代数簇的拓扑学。特别强调的是新的拓扑不变量的发展(例如，不同版本的基元倒置层)，以及共形场理论中出现的结构(回路空间的几何)。这项工作结合了来自理论物理的想法和来自几何学的其他想法，使用了同样多样化的方法。

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.