Algebraic Geometry Seminar: Dusty Ross

The Gopakumar-Marino-Vafa formula, proven almost ten years ago, evaluates certain triple Hodge integrals on moduli spaces of curves in terms of Schur functions.  It has since been realized that the GMV formula is a special case of the Gromov-Witten/Donaldson-Thomas correspondence for Calabi-Yau threefolds.

In this talk, I will introduce an orbifold generalization of the GMV formula which evaluates certain abelian Hodge integrals in terms of loop Schur functions.  I will introduce local Z_n gerbes over the projective line and show how the gerby GMV formula can be used to prove the GW/DT correspondence for this class of orbifolds.  With the remaining time, I will sketch the main ideas in the proof of the formula and discuss generalizations to other geometries.