Algebraic Tolopology and Quantum Field Theory

DMS-0210822丹尼斯·P·沙利文处理多参数或多维问题的一种有效的数学技术是组合或代数拓扑。在该领域中，与约束有关的几何对象，称为圈，被分成形变或同调类，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，这些结构中的一些已经出现在理论物理中，试图以形式主义的方式描述量子现象的逐项模型。主要研究人员最近在填充空间(时间)模型的弦空间(开放的和封闭的)中发现了相关的代数拓扑结构。该奖项将赞助研究，从概念上阐明理论量子物理中代数拓扑的出现，并将这些研究的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.