Colloquium
3:30 p.m., Friday
Math 100
Stephen Gustafson
Courant Institute
Some Mathematical Problems in the GinzburgLandau Theory of Superconductivity
In the GinzburgLandau theory (1950), the state of a
superconductor
is described by solutions of a pair of nonlinear PDEs called the
GinzburgLandau equations. Abrikosov (1957) observed that a
fundamental role is played by a family of symmetric solutions known
as vortices, which are classified by a topological degree, and which
represent localized defects in the superconductor. Recently, the
GinzburgLandau theory has received a lot of attention from
mathematicians.
I will describe some of the interesting issues, focusing on vortices
and their dynamics. In particular, I will present results which
settle an old conjecture about how vortex stability depends on the
topology, and on the nature of the superconducting material.
