EVENT DETAILS AND ABSTRACT

Title: Vertex algebras and the formal loop space
Speaker: Professor M. Kapranov
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Abstract:

The talk will be based on a joint work with E. Vasserot.

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.