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On modular forms and system of differential equations

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Younes Nikdelan
Universidade do Estado do Rio de Janeiro/MPIM
Don, 01/07/2021 - 15:00 - 16:00
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The aim of this talk is to give a general report of my recent works. As I know, the first appearance of
the systems of ODEs which accept a solution as modular forms goes back to Darboux-Halphen
and then Ramanujan. We will have a brief look at the Ramanujan system, which is also known
as the Ramanujan relations between the Eisenstein series, and use it to explain the general ideas
behind my work. In particular, we observe that the Ramanujan system can be seen as a vector field
on an enhanced moduli space of a certain family of elliptic curves. In this way, we will apply this
method to the family of Calabi-Yau varieties and discover some new system of ODEs whose
solutions are not any more classical modular forms, but their q-expansions are somehow related
with some known functions coming up from theoretical physics, mirror symmetry. Our goal is
to study the space generated by these solutions, which are called Calabi-Yau modular forms.
Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (

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