Speaker
Israel Michael Sigal: University of Toronto
Abstract
The Chern-Simons-Ginzburg-Landau (CSGL) model proposed by Zhang, Hanson and Kivelson (ZHK) provides a system of nonlinear evolution PDEs describing a range of phenomena related to the fractional quantum Hall effect (FQHE). In particular, CSGL equations are supposed to have vortex solutions describing quasiparticle anyonic excitations in quantum Hall fluids. Similar equations and their non-abelian generalizations appear also in some models of particle physics in connection with the topological quantum field theory. CSGL have a natural geometrical interpretation as coupled equations for the sections and connections of line bundles.
In this talk, I describe the basic properties of the CSGL system, its key solutions – Chern-Simons vortices and vortex lattices – present some open problems, and say a few words on the extension of this system to Riemann surfaces.