Topological Solitons and their Moduli Spaces

拓扑孤子及其模空间

• 批准号: 2119350
• 金额: --
• 依托单位: University of Kent
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2119350
• 关键词: Topological; Solitons; their; Moduli; Spaces

"Topological solitons are smooth, localised, finite energy solutions in non-linear field theories. The soliton number is conserved due to a topological constraint, such as a winding number or a non-trivial Chern class. Originally motivated from physics, these solitons give rise to interesting mathematical objects which can be studied using differential geometry and algebraic topology.The PhD project mainly focusses on Abelian vortices on hyperbolic space as well as CP^1 lumps and RP^2 lumps where the domain is a general two dimensional manifold. Geometric properties of the soliton moduli space will be derived. Forexample, in some special cases, explicit formulas for metric and Ricci curvature can be calculated and studied. In other cases, global information such as the total volume, diameter and the total curvature can be computed. Furthermore,different types of dynamics of topological solitons will be studied. The most well-known dynamics is geodesic flow. Recently, a novel type of dynamics, known as Ricci magnetic geodesic motion, has been discovered. The necessary computations will mainly be analytical. However, the resulting formulas can become lengthy so that the use of a suitable symbolic computer algebra package such as Maple is essential. Some numerical calculations may alsobecome necessary.References:[1] N.S. Manton and P.M. Sutcliffe, Topological Solitons, Cambridge University Press, 2004."

“拓扑唯一的唯一唯一的唯一局部，有限的能量解决方案在非线性野外理论中。由于拓扑数量或非平凡的Chern类，孤儿数量是保守的。这些孤儿最初是从物理学上动机的，最初可以使用有趣的数学对象来使用差异的数字来研究，而这些数学的数学是对差异的景点。双重空间以及CP^1块和RP^2块是二维歧管的一般歧管，在某些特殊情况下，可以在其他情况下进行整体信息，在某些情况下，可以计算指标和RICCI的明确公式。此外，将研究最著名的动力学的拓扑孤子动力学。必要的计算将主要是分析性的。但是，所得的公式可以冗长，因此使用合适的符号计算机代数软件包（例如枫木）至关重要。引用：[1] N.S.曼顿和下午萨特克利夫（Sutcliffe），《拓扑唯一》，剑桥大学出版社，2004年。”