Ramanujan Auditorium

Symplectic geometry and vortices

Christopher Woodward

Rutgers University, USA

Vortices are solutions in gauge theory to an equation
involving a connection and section of a vector bundle, which generalize the anti-self-dual Yang-Mills equations on a four-manifold.  I will talk about some recent results on classification of vortices on the plane, joint with Venugopalan, of Narasimhan-Seshadri type, and sketch some applications to holomorphic curves in symplectic quotients.