An introduction to Frobenius manifolds and primitive forms III

Abstract

The notion of Frobenius manifold was essentially found by Kyoji Saito, and axiomatized by Dubrovin. Frobenius manifolds play an important role in algebraic geometry, singularity theory and mirror symmetry. Based on mirror symmetry, it is expected that there exists a structure of Frobenius manifold on the space of stability conditions on a certain triangulated category. In particular, we expect that stability conditions for ADE singularity should be given by a period mapping associated to a primitive form. In the lecture series, I will explain the following contents: 1. Basics of Frobenius manifolds. 2. Basics of primitive forms and period mappings associated to it. 3. An (expected) relationship between the space of stability conditions and Frobenius manifold for ADE singularities.