Description
Mathematics Colloquium.
Speaker: Hossein Movasati.
Affiliation: IMPA, Rio de Janeiro.
Date and Time: Wednesday 18 December, 4:00 pm - 5:00 pm.
Venue: Room 216, Department of Mathematics.
Title: Ramanujan's relations between Eisenstein series.
Abstract: In 1916 S. Ramanujan discovered three identities involving the
Eisenstein series $E_2,E_4,E_6$ and their derivatives. This can be seen as
a vector field in the moduli space of an elliptic curve $E$ enhanced with
a certain frame of the de Rham cohomology of $E$. For this one needs
algebraic de Rham cohomology, cup product and Hodge filtration developed
by Grothendieck and Deligne among many others. Viewed in this way,
Ramanujan's differential equation can be generalized to an arbitrary
projective variety. If time permits I will explain two generalizations of
this picture in the case of Abelian varieties and Calabi-Yau threefolds.