Speaker: Hossein Movasati (BIMSA)
Time: 2025-10-23 16:00-17:30
Location: 1610, SIMIS
Zoom Meeting ID:832 4329 1539 Passcode:SIMIS
In this talk I will consider a moduli space of projective varieties enhanced with a certain frame of their cohomology bundles. In many examples such as elliptic curves, abelian varieties, Calabi-Yau varieties, and conjecturally in general, this moduli space is a quasi-affine scheme over ${\mathbb Z}[\frac{1}{N}]$ for some natural number $N$. The ring of global regular functions on this quasi-affine variety is called the ring of CY modular forms and it gives us natural generalizations of modular and quasi-modular forms.
In the case of Calabi-Yau threefolds, it includes the genus $g$ topological string partition function encoding genus $g$ Gromov-Witten invariants.
We can also rewrite the BCOV anamally equation using certain vector fields on this moduli space which are algebraic incarnation of differential equations of automorphic forms. After taking modulo $p$ of this moduli space for $p$ coprime with $N$, I will discuss an outline of a project how to prove the $p$-integrality of Calabi-Yau modular forms beyond the established cases of hypergeometric Calabi-Yau varieties (after Yau, Lian, Krattenthaler among many others).
The talk is based on my book “Modular and Automorphic Forms & Beyond, Monographs in Number Theory, World Scientific (2021)” in which the Tupi name ibiporanga (pretty land) for such a moduli space is suggested.
English 
简体中文