Preface -- Contents -- Bifurcation Problems for Ginzburg-Landau Equations and Applications to Bose-Einstein Condensates -- 1 The Ginzburg-Landau system in dimension 1 -- 1.1 Introduction -- 1.2 Symmetric solutions -- 1.3 Asymmetric solutions -- 2 The Ginzburg-Landau model in dimension 2 -- 2.1 Introduction -- 2.2 The bifurcation diagrams -- 2.3 Uniqueness for small d -- 3 Vortices in Bose-Einstein condensates -- 3.1 Introduction -- 3.2 Mathematical formulation -- 3.3 Asymptotic expansion of the energy -- 3.4 2d case -- 3.5 3d case -- 3.6 Vortex bending -- 3.7 Conclusion -- References -- Vortex Analysis of the Ginzburg-Landau Model of Superconductivity -- Introduction -- 0.1 History -- 0.2 The Ginzburg-Landau model -- 0.3 Adimensionalizing -- 0.4 Dimension reduction -- 0.5 Notation -- 1 Minimization of the Ginzburg-Landau Functional -- 1.1 Gauge invariance -- 1.2 The Coulomb gauge -- 1.3 Minimization of the Ginzburg-Landau energy -- 1.4 Euler-Lagrange equations -- 2 Introduction to Critical Fields in R2 -- 2.1 Pure states -- 2.2 Critical line Hc2 -- 2.3 Critical line Hc1 -- 2.4 Phase diagram -- 3 Mathematical Preliminaries -- 3.1 Degree theory -- 3.2 The co-area formula -- 3.3 Sard's theorem -- 4 The Ball Construction Method -- 4.1 S1-valued maps on perforated domains -- 4.2 Vortex balls -- 5 The Jacobian Estimate -- 5.1 Main theorem -- 5.2 The case

5 On potentials which are functions of the distance to a curve -- 6 The general "circular-well" potential -- References -- Existence Results on Ginzburg-Landau Equations -- Introduction -- Lecture 1: Asymptotic analysis for GL solutions and the renormalized energy -- Lecture 2: Existence of GL solutions with prescribed vortices -- Lecture 3: Multiplicity results on GL equation -- Lecture 4: Other existence results -- 1. Non simply connected domains -- 2. Superconductivity -- References -- A Survey on Ginzburg-Landau Vortices of Superconducting Thin Films* -- 1 Introduction -- 2 Vortices of simplified models -- 3 Simplified Ginzburg-Landau models for thin films -- 4 Ginzburg-Landau vortices for superconductivity -- 5 Ginzburg-Landau vortices for superconducting thin films -- References -- On the Hydro-dynamic Limit of Ginzburg-Landau Wave Vortices -- 1 Introduction -- References -- Singular Sets of the Landau-Lifshitz System* -- 1 Introduction -- References -- Analysis of Ginzburg-Landau Models for Type I Superconductivity* -- 1. Models -- 2. Free boundary problem in superconductivity -- 3. The problem in one dimensional case -- 4. The problem in two dimensional case -- 5. On a 3-D free boundary problem involving mean curvature and kinetic undercooling -- References -- Ferromagnets and Landau-Lifshitz Equation -- 1 Introduction -- 2 Existence and stability -- 3 Non-existence -- 4 Proof of existence -- 5 Non-existence to Landau-Lifshitz equation -- References.