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.

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

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