Frobenius manifolds from Lie theory

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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.