Emily Cliff (Oxford): One- and two-dimensional factorization structures on the Hilbert scheme of points of a surface
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 algebra over any curve C. Moreover, ideas from physics suggest that we should also look for a two-dimensional factorization algebra associated to Hilb(X). In this talk, we will define factorization spaces and factorization algebras; then we show how we can use Hilb(X) to produce examples of each over curves and surfaces. No prior knowledge of factorization will be assumed.