Seminar

Emily Cliff, Oxford University

Title: Constructing factorization spaces and chiral algebras from the Hilbert scheme of points

Abstract:
Given a complex surface X, Nakajima and Grojnowski have shown that the cohomology H of Hilb(X) is naturally a representation of the Heisenberg Lie algebra modelled on the cohomology of X, and is isomorphic as a representation to the Fock space. It follows that H acquires a canonical structure of vertex algebra, and hence that we can associate to H a factorization or chiral algebra over any curve C. Motivated by this result, we attempt to construct this factorization algebra directly using the Hilbert scheme of X. In this talk, we will introduce the notions of factorization spaces and factorization algebras; then we show how we can use Hilb(X) to produce examples of each over curves and surfaces.