On some Dubrovin–Frobenius Manifolds

Student: Anastasiia Arbanas

Educational Programme: Joint Bachelor's Programme with the Centre for Teaching Excellence (Bachelor)

Year of Graduation: 2025

This work considers algebraic structures, namely Frobenius algebras, and their connection to Dubrovin–Frobenius manifolds. The construction of a superpotential for semisimple Frobenius manifolds is studied. The main focus is on constructing a Frobenius structure for a given potential: a program has been implemented to compute the multiplication tensors c_γ^(αβ) and to verify associativity. A detailed analysis of the two-dimensional potential is carried out based on existing results, and a three-dimensional example is examined.

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