Mathematical Sciences: "Geometry of Charateristic Classes"

[504237] McLaughlin提出的研究是微分拓扑学和数学物理的结合。更具体地说，它处理了所谓的Teichmuller空间上的weuss - zumino - witten向量束，并试图给出该束上的投影平坦连接的严格公式。近年来，人们在拓扑学和数学物理之间发现了一些意想不到的关系。如果完全成功，这项最初由量子场论问题驱动的研究可能会为三维空间和结理论的研究带来新的曙光。

9504237 McLaughlin The proposed research lies in the interface of differential topology and mathematical physics. More specifically, it deals with the so called Wess-Zumino-Witten vector bundle on Teichmuller space and is an attempt to give a rigorous formula for the projectively flat connection on this bundle. In recent years several unexpected relations between topology and mathematical physics have been discovered. If completely successful, the proposed research - which is originally motivated by problems in quantum field theory - will likely shed a new light on the study of 3-dimensional spaces and knot theory.