Frobenius manifolds from Lie theory

李理论中的弗罗贝尼乌斯流形

• 批准号: 2279475
• 金额: --
• 依托单位: University of Glasgow
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2279475
• 关键词: Frobenius; manifolds; Lie; theory

Frobenius manifolds is an important mathematical structure with relevance to many areas including theoretical physics, theory of integrable systems, geometry and algebra. The current project belongs to the broad area of mathematical physics. Particular Frobenius manifolds which will be investigated come from Lie theory which is a key mathematical concept. These Frobenius manifolds are known to satisfy some interesting properties but many aspects are not yet developed. The project aims to uncover more structures related to this important class of Frobenius manifolds. This would require developing and extending methodology known in some related examples of Frobenius manifolds which is based on Landau-Ginzburg superpotentials. Given fundamental nature of the Frobenius manifolds under investigations one may expect applications and connection of the research with other areas including integrable systems.

Frobenius流形是一种重要的数学结构，涉及理论物理、可积系统理论、几何和代数等诸多领域。目前的项目属于数学物理的广阔领域。我们将要研究的特殊的Frobenius流形来自于李理论，这是一个关键的数学概念。已知这些Frobenius流形满足一些有趣的性质，但许多方面尚未开发。该项目旨在揭示更多与这类重要的Frobenius流形相关的结构。这将需要发展和扩展基于朗道-金兹堡超势的弗罗贝尼乌斯流形的一些相关例子中已知的方法。考虑到所研究的Frobenius流形的基本性质，人们可以期望该研究与包括可积系统在内的其他领域的应用和联系。