权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Geometry of vector bundles and moduli spaces of instantons

向量丛的几何和瞬子模空间

基本信息

批准号：
402489-2011
负责人：
Charbonneau, Benoit
金额：
$ 1.17万
依托单位：
University of Waterloo
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2018
资助国家：
加拿大
起止时间：
2018-01-01 至 2019-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=647203
关键词：
Geometry vector bundles moduli spaces

项目摘要

This research program is concerned with understanding the topology and geometry of various moduli spaces of vector bundles equipped with special structures. Such a program lies in the mathematical field of differential geometry, the study of calculus and differential equations on manifolds, and more specifically it lies in the field of gauge theory, the study of vector bundles and connections.****There have been ongoing efforts in the mathematics and physics worlds to classify Yang-Mills instantons, which are connections whose curvature minimizes a certain energy. The focus of this research program is to do this classification on certain non-compact manifolds, that is to gain knowledge about the geometry and topology of the spaces of instantons living on those spaces, modulo natural equivalences. Ideally, one could express this space, a space of solutions to a difficult partial differential equation, in terms of solutions to more tractable equations (ordinary differential equation, algebraic equation). One then describes the geometry of the starting space through such a lens. Working on a non-compact base manifold creates serious difficulties and tools must be developed to address them.****Overcoming these difficulties and providing information about these moduli spaces allows a better understanding of the physics of instantons, provides valuable information about the underlying manifolds, and is interesting math on its own sake.**********************

该研究项目涉及理解具有特殊结构的向量丛的各种模空间的拓扑和几何。这样的程序属于微分几何的数学领域，即流形上的微积分和微分方程的研究，更具体地说，它属于规范理论领域，即矢量丛和连接的研究。****数学和物理界一直在努力对杨-米尔斯瞬子进行分类，杨-米尔斯瞬子是曲率最小化特定能量的连接。该研究计划的重点是对某些非紧流形进行分类，即获得有关存在于这些空间上的瞬子空间的几何和拓扑的知识，模自然等价。理想情况下，我们可以用更容易处理的方程（常微分方程、代数方程）的解来表达这个空间，即困难的偏微分方程的解空间。然后通过这样的透镜描述起始空间的几何形状。研究非紧基流形会产生严重的困难，必须开发工具来解决这些问题。****克服这些困难并提供有关这些模空间的信息可以更好地理解瞬子的物理原理，提供有关基础流形的有价值的信息，并且其本身就是有趣的数学。************************