Mathematics

The aim of the course is to introduce the audience to the analytic theory of Dubrovin-Frobenius manifolds.

The theory of Frobenius manifolds was constructed by B. Dubrovin to formulate in geometrical terms the WDVV equations of associativity of 2D topological field theories. It has links to many branches of mathematics, like singularity theory and reflection groups, algebraic and enumerative geometry, quantum cohomology, theory of isomonodromic deformations, boundary value problems and Painlev´e equations, integrable systems and non-linear waves.

In this course, we will give the general setting of Dubrovin-Frobenius manifolds, and then we will concentrate on the study of their moduli, namely the monodromy data of a flat connection defined on the manifold.

We will see some examples and applications. Prerequisites: Basic differential and Riemannian geometry, complex functions, theory of differential equations in the complex domain and isomonodromy deformations.