Computational Algebra Seminar

Computational Algebra Seminar

Helena Verrill
Copenhagen

Picard-Fuchs equation for families of elliptic curves

Thursday 3rd March, 3-4pm

Eastern Avenue Tutorial Room 404

The Picard-Fuchs differential equation of a family of varieties is useful for describing the variation of Hodge structure of the family. I will give the definition of the Picard-fuchs equation in general, and describe its computation. I will give examples for the case of families of elliptic curves and families of K3 surfaces.

I will concentrate on the case of modular families of of elliptic curves, which leads to differential equations for modular forms, and if there is time I will also describe a relationship between a solution of the Picard-Fuchs equation and equation the L-series of the ambient space in certain cases.