Frobenius structures from Calabi-Yau categories

Primitive forms were introduced by K. Saito in his construction of period mapping in the unfolding space of singularities. The Hodge theoretic structure involved in this construction is known as the semi-infinite Hodge structure introduced by Barannikov and Kontsevich. Following Kontsevich's proposal in his 1994 ICM address, we shall discuss the appearance of such structures in the categorical contexts, as well as a few open problems in this direction.