Frobenius manifolds from Lie theory

Frobenius流形是一种重要的数学结构，与理论物理、可积系统理论、几何和代数等领域都有着密切的联系。目前的项目属于数学物理的广泛领域。特别是Frobenius流形，将被调查来自李理论，这是一个关键的数学概念。这些弗罗贝纽斯流形已知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的方法，已知在一些相关的例子Frobenius流形，这是基于朗道-金兹伯格超势。考虑到研究中的Frobenius流形的基本性质，人们可以期望将研究与包括可积系统在内的其他领域联系起来。

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.