Algebraic Tolopology and Quantum Field Theory

DMS-0210822 Dennis P. Sullivan处理多个参数或维度问题的有效数学技巧之一是组合拓扑学或代数拓扑学。 在该领域中，几何对象，称为循环，与constraintsgrouped到变形或同源类，然后联合收割机和分解在各种组合，以定义代数结构的丰富性，挑起理论研究在自己的权利，各种代数结构。最近，这些结构中的一些已经出现在理论物理学中，试图以形式主义来描述量子现象的逐项模型。在合作中，首席研究员最近发现了填补空间（时间）模型的弦（开和闭）空间中的相关代数拓扑结构。 该奖项将赞助调查，从概念上澄清理论量子物理学中代数拓扑的发生，并将这些调查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.