Four Lectures on Primitive Forms. 4th lecture: Existence and the construction of primitive forms

Abstract
A primitive form is a family of differential forms of top-degree defined on a family of open complex varieties. It was introduced as a higher dimensional generalization of the elliptic integral of the first kind, and its period integral over vanishing cycles are expected to introduce new class of automorphic forms. In the last decade, it was getting clear that a primitive form is an object in complex geometry which is mirror to the Gromov-Witten invariants in symplectic geometry. From this new categorical view point, there appear several new trials to reconstruct primitive forms in a categorical manner in a context of «non-commutative Hodge theory». In the present series of lectures, I restrict myself to the view point of the classical complex geometry. We do not assume any prerequisite knowledge to the audiences except for basic mathematics. However, some knowledge of complex analytic geometry may be helpful. Schedule of lectures
The lectures take place at the Faculty of Mathematics (Vavilova 7, near the metro station «Leninsky Prospect»). Fri, 17.06, room 311, 17:00. 1st lecture: Local analytic geometry of unfolding of singularities. Tue, 18.06, room 1001, 17:00. 2nd lecture: Semi-infinite filtered cohomology and higher residues. Wed, 19.06, room 1001, 17:00. 3rd lecture: Primitive forms and induced flat (Frobenius) structure. Thu, 20.06, room 311, 17:00. 4th lecture: Existence and the construction of primitive forms. Fri, 21.06, room 311, 17:00 is a reserved time for possible extensions.