1.In the theory of superconductors of Type II in the Ginzburg-Landau model, there is a critical field called the second critical field where superconductivity goes from being a bulk to a boundary phenomenon. A precise mathematical definition is hard to give but one can observe this phenomenon in suitable limit situations. In this talk I will describe recent work both in 2 and 3 dimensions on the ground state energy density for the Ginzburg-Landau model in the Type II limit and show how the transition to boundary superconductivity is evident from the energy density. This is joint work with Ayman Kachmar.

2. We consider 2 dimensional superconductors in the Ginzburg-Landau model. In the regime where superconductivity of Type II superconductors is a boundary phenomenon it was proved by Pan that superconductivity is uniformly distributed in energy along the boundary. However, the calculation of the constant appearing in this energy density, i.e. the strength of the boundary superconductivity is only conjectures. In this talk we will describe how this non-linear problem can be reduced to the study of a 1-dimensional spectral problem and we will give some spectral results on this 1D problem. This is joint work with Bernard Helffer and Mikael Persson.