Michigan State University, East Lansing
& IAS, Princeton
Elliptic PDEs and Bifurcations of Holomorphic Curves
The first part of this talk will be an overview of the
analytic
approach to Gromov-Witten invariants.
That analysis is
particularly interesting when applied to holomorphic
maps into a
Calabi-Yau 3-fold. I will describe
recent joint work with E. Ionel
which, building on work of Taubes, uses PDE
methods to give a
geometric accounting of the holomorphic curves,
their covers, and
their bifurcations in Calabi-Yau 3-folds.
The resulting picture
gives a specific geometric interpretation, and
partially solves the
'Gopakumar-Vafa conjecture' which emerged
from string theory.