John Alexander Cruz Morales (Max-Planck-Institut, Bonn)
Frobenius manifolds, introduced by Dubrovin, are flat Riemannian manifolds with a certain compatible multiplicative structure on the tangent space. They occur naturally in symplectic topology, more specifically in quantum cohomology. Given a Frobenius manifold, Dubrovin constructed a related object to
it that satisfies almost all the axioms of a Frobenus manifold. He called this object an almost Frobenius manifold and the relationship between these two objects is known as almost Frobenius duality. We will present the case of the Frobenius manifold given by the quantum cohomology of projective spaces (discussed by Dubrovin) and give some ideas on how this could be extended to the case of weighted projective spaces. If time permits, relations to mirror symmetry will be also discussed.
