Xuanzhong Dai (RIMS): On recent progress on the chiral de Rham complex and modular forms

The Chiral de Rham complex introduced by Malikov et al. is a sheaf construction of vertex algebras on any smooth manifold or nonsingular algebraic variety. Applying this technique to the upper half plane, we obtain a quantization of modular forms, which recovers the Rankin-Cohen brackets, a family of bilinear operations on modular forms. It has long been speculated that the Rankin-Cohen brackets are connected to vertex operator algebras, as initially proposed by W. Eholzer, Y. Manin, and D. Zagier. Our construction naturally inherits a vertex algebra structure, with the vertex operation fully determined by a slight modification of the Rankin-Cohen brackets.