Chiral de Rham complex on the upper half plane and modular forms

2021/02/04 Thu 10:30 - 12:00
Xuanzhong Dai
Fudan University

Chiral de Rham complex constructed by Malikov, Schechtman and Vaintrob in
1998, is a sheaf of vertex algebras on a complex manifold. For any congruence
subgroup $\Gamma$, we consider the $\Gamma$-invariant global sections of the chiral
de Rham complex on the upper half plane, which are holomorphic at all the cusps. We
show that it contains an $N=2$ superconformal structure and we give an explicit
lifting formula from modular forms to it. As an application, the vertex algebra
structure modifies the Rankin-Cohen bracket, and the modified bracket with the
Eisenstein series involved becomes nontrivial between constant modular forms.

This will be a zoom seminar.

zoom URL:
passcode: The order of the Mathieu group $M_{22}$