Mathematical Sciences: Geometric Questions in Algebraic Topology

8901879 Mann 曼教授将研究两个项目在代数 拓扑，除了它们的拓扑兴趣之外， 数学物理中的应用，非线性部分 微分方程和线性控制理论。 第一个项目，代表与教授的联合工作 C.博耶，继续教授博耶正在进行的计划 和曼研究几何和拓扑的模空间的 瞬子和单极子， 杨-米尔斯-希格斯规范理论的几何表述 的 该计划中开发的技术可应用于其他 模的问题，这也将被调查。 第二个项目，代表与教授的联合工作 R. J. Milgram试图推广F.R. Cohen，R.L. Cohen，B.M.曼恩和R. J.米尔格拉姆 有理函数的一般情况从黎曼球面到 格拉斯曼流形和旗流形。 这种空间的拓扑学 在几个领域都很重要，包括线性控制理论， 本项目的研究成果将在实际应用中得到应用 数学的其他领域。

8901879 Mann Professor Mann will investigate two projects in algebraic topology which, in addition to their topological interest, have applications in mathematical physics, non-linear partial differential equations, and linear control theory. The first project, representing joint work with Professor C. P. Boyer, continues the ongoing program of Professors Boyer and Mann to study the geometry and topology of moduli spaces of instantons and monopoles which arise in the differential geometric formulation of Yang-Mills-Higgs gauge theories. The techniques developed in this program have applications to other moduli problems which will also be investigated. The second project, representing joint work with Professor R.J. Milgram, attempts to extend the results of Professors F.R. Cohen, R.L. Cohen, B.M. Mann, and R.J. Milgram on the more general case of rational functions from the Riemann sphere to Grassmannians and flag manifolds. The topology of such spaces is important in several areas, including linear control theory, and the results of this project will be useful in applications to other areas of mathematics.