Algebraic Geometry Seminar
Erik Carlsson
Northwestern University
Vertex Operators and Hilbert Schemes
Abstract: For a long time people have recognized that there is a (perhaps mysterious) connection between
the cohomology of the Hilbert scheme of points on a surface and 2-d conformal field theory. At a
minimum, the direct sum \bigoplus_n Hilb_n X is isomorphic to some Fock space in CFT, and the
important operators on the CFT side make for valuable auxilliary gadgets on the Hilbert scheme
side. I'll give a geometric construction for the ``vertex operator'' in CFT for any smooth
surface, and show how this can be used for some simple Hilbert scheme calculations.
Thursday November 13, 2008 at 4:00 PM in SEO 636