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.
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