Mathematical Physics Seminar

I will introduce the GL equations and give a very brief discussion of solutions to the critical case where it is possible to reduce the second order equations to a first order of Bogomolny type. The focus of this talk, however, will be on the general case of GL equations via bifurcation theory. A main difficulty is to reduce the dimension of solutions to the linearized problem to 1 so that one can more easily understand the location of vortices of these solutions. I will present a discussion on this problem. Finally, if time permits, I will discuss generalization of GL equations to line bundles of Riemann surfaces.