Mathematical Sciences: Complex Geometry and Mathematical Physics

两位研究者将研究各种几何结构，这些几何结构起源于数学物理和复杂几何。这些包括射影代数流形，复流形，四元数Kahler流形和超流形。该研究将包括与四元数Kahler约简、自对偶流形和四元数Kahler结构的扭转表示相关的动量映射的研究。本文将利用计算机研究二维杨-米尔-希格斯方程的静态自对偶解的动力学。这两位研究者将继续研究新的“超几何”，这是规范理论的一部分，旨在理解宇宙学和亚原子物理学之间的关系。一个将继续在奈杰尔·希钦的框架下研究扭曲几何。第二部分将使用“四元数商”进一步推导出具有异常自旋完整的完全非紧流形的知识。这是叶理的一个性质，用来衡量它们的剪切倾向。

The two investigators will study a variety of geometric structures which have their origins in mathematical physics as well as complex geometry. These include projective algebraic manifolds, complex manifolds, quaternionic Kahler manifolds, and supermanifolds. The investigation will include a study of the momentum mapping in connection with quaternionic Kahler reduction, self-dual manifolds, and the twistor representation of quaternionic Kahler structures. The dynamics of the static self- dual solutions of the two-dimensional Yang-Mills-Higgs equations will be studied with the use of a computer. The two investigators will continue their studies of the new "supergeometry" which was created as part of gauge theory to understand the relationship between cosmology and subatomic physics. One will continue his work on the twistor geometries in Nigel Hitchin's framework. The second will use "quaternionic quotients" to derive further knowledge of complete noncompact manifolds with unusual spin holonomy. This last is a property of foliations and measures their shearing tendencies.