Factorization structures on the Hilbert scheme of points on a surface

Emily Cliff (Oxford)

Nakajima and Grojnowski have shown that the cohomology H of HilbX 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. In this talk we outline some of the key ideas involved in identifying H with the Fock space; then we define the notion of a factorization algebra and introduce a way of directly constructing a factorization algebra A from HilbX. Finally, we conjecture that A is isomorphic to the factorization algebra obtained via the Fock space construction, and discuss some strategies for proving this. No prior knowledge of vertex algebras or factorization algebras is assumed.

Tuesday, September 16th, at 4:00pm in HBH 227

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