Algebraic Tolopology and Quantum Field Theory

处理多个参数或维度问题的有效数学技术之一是组合拓扑，或代数拓扑。在这个领域中，与约束相关的几何对象，称为循环，被分组为变形类或同调类，然后以各种组合组合和分解，以定义如此丰富的代数结构，从而引发对各种代数结构本身的理论研究。最近，这些结构中的一些出现在理论物理学中，试图用形式主义来描述量子现象的逐项模型。在合作中，首席研究员最近在填充空间（时间）模型的弦（开放和封闭）空间中发现了相关的代数拓扑结构。该奖项将资助研究，从概念上澄清代数拓扑在理论量子物理学中的出现，并将这些研究结果与新的弦代数联系起来。

DMS-0210822Dennis P. SullivanOne of the effective techniques of mathematics for dealing with problems of several parameters or dimensions is combinatorial, or algebraic, topology. In that field, geometric objects, called cycles, associated to constraintsare grouped into deformation or homology classes which then combine and decompose in various combinations to define algebraic structures of such richness to provoke a theoretical study in the own right of a variety of algebraic structures. Recently some of these structures have appeared in theoretical physics in the attempted formalism to describe term by term models for quantum phenomena.In collaboration, the principal investigator has recently discovered related algebraic topology structures in the space of strings (open and closed) filling up a space (time) model. This award will sponsor investigations to conceptually clarify the occurance of algebraic topology in theoretical quantum physics and to relate the results ofthese investigations to new string algebra.