Moduli spaces of sheaves and the boson-fermion correspondence                     
-- Alistair Savage, October 3, 2008

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Abstract: The boson-fermion correspondence is a fundamental
result in mathematical physics that relates the state spaces of
fermions (particles with half-integer spin) and bosons
(particles with integer spin).  It is also one of the basic
examples of the use of vertex operators in representation
theory.  We will describe how one can give a geometric
realization of the (r-colored) boson-fermion correspondence
using the equivariant cohomology of the moduli space of framed
torsion-free sheaves on the projective plane.  In this
framework, the vertex operators are realized as Chern classes
of vector bundles.  This is joint work with Anthony Licata.