Mathematical Sciences: Research in Index Foliation Theory

9504084坎伯拟议的研究是指数和层理理论及其在数学物理中的应用。所提出的问题是抽象指数理论中的核心问题，在度量理论和异常方面具有重要的应用。研究人员早些时候介绍的叶理减少技术可能会被证明与新发现的Seiberg-Witten单极子方程有有趣的联系。分叶理论试图理解常微分方程解空间的整体行为；指数理论将整数和其他容易识别的量赋给这些空间，并旨在通过它们的指数来区分不同的空间。这里开发的技术和结果继续在数学物理的各个部分得到应用。

9504084 Kamber The proposed research is in index and foliation theory with applications to mathematical physics. The proposed problems are central problems in the abstract index theory and have significant applications to gauge theories and anomalies. Foliation reduction techniques introduced earlier by the investigator may prove to have interesting connections to the newly discovered Seiberg-Witten monopole equations. Foliation theory seeks to understand the global behavior of spaces of solutions to ordinary differential equations; index theory assigns integers and other easily identifiable quantities to these spaces and aims to distinguish different spaces by means of their indices. The techniques and results developed here continue to find applications in various parts of mathematical physics.