Calabi–Yau dg categories to Frobenius manifolds via primitive forms

It is one of the most important problems in mirror symmetry to construct functorially Frobenius manifolds from Calabi–Yau dg categories since the Kontsevich's homological mirror symmetry should imply the classical one, the isomorphism of Frobenius manifolds between the one from Gromov–Witten theory and the one from the deformation theory. This talk gives an approach to this problem based on the theory of primitive forms. Under a formality assumption, we shall construct formal primitive forms, which enable us to have formal Frobenius manifolds.