报告时间：2021年4月12日  14:00-15:00

报告地点： 精正楼二楼报告厅

报告人： 戴煊中 (上海数学中心) 

报告摘要：

Chiral de Rham complex is a sheaf of vertex algebras on any complex manifold or nonsingular variety, which is introduced by Malikov, Schechtman and Vaintrob in 1998. Our main object is the chiral de Rham complex on the upper half plane. We show that $SL(2, \mathbb R)$ acts as vertex algebra automorphisms on the global sections $\Omega^{ch}(\mathbb H)$. Especially, for any congruence subgroup $\Gamma$, we consider the subspace of $\Omega^{ch}(\mathbb H)$ consisting of $\Gamma$-invariant global sections that are holomorphic at all the cusps, denoted by $\Omega^{ch}(\mathbb H,\Gamma)$. We show that it is still a vertex operator algebra with an $N=2$ superconformal structure and we also give an explicit lifting formula from modular forms to it. As an application, we will modify the Rankin-Cohen bracket such that the modified bracket is compatible with the vertex algebra structure of $\Omega^{ch}(\mathbb H,\Gamma)$, and the modified bracket with the Eisenstein series involved becomes nontrivial between constant modular forms.

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邀请人：白占强, 董超平