Erik Carlsson : Vertex Operators and Hilbert Schemes

Posted by , part of the Algebraic Geometry Seminar.

At

Nov. 13, 2008, 4 p.m.

In

SEO 636

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.