Title: Vertex algebras and the formal loop space
Speaker: Professor M. Kapranov
The talk will be based on a joint work with E. Vasserot.Date: Tuesday, November 14, 2000
For an algebraic variety X we construct an ind-scheme LX which is an algebro-geometric version of the free loop space of X. We show that LX has the structure of a "chiral semigroup", which is a nonlinear analog of the structure of a chiral algebra introduced by Beilinson and Drinfeld to geometrize the theory of vertex operator gebras. This implies that any natural linear construction applied to LX, produces a VOA. In particular, we get a direct geometric construction, in terms of LX, of the chiral de Rham complex of X and of the structure of a VOA on this complex.