In the first part of the talk, I will review key results on the asymptotic behavior of the simplified Ginzburg-Landau energy (no fields) and its minimizers. Then, using a combination of tools from Gamma-convergence, geometric measure theory and gradient flow analysis of the associated parabolic Ginzburg-Landau system, I will discuss a new result on construction of unstable critical points for GL on a 3d Riemannian manifold that concentrate on a stationary (non-length minimizing) geodesic. This is joint work with Andrew Colinet and Bob Jerrard.
