We prove the Landau–Ginzburg mirror symmetry conjecture between invertible quasihomogeneous polynomial singularities at all genera. That is, we show that FJRW theory (LG A-model) of such a is equivalent to Saito–Givental B-model) polynomial.

A large class of (0,2) Calabi-Yau σ-models and Landau-Ginzburg orbifolds are shown to arise as different “phases” of supersymmetric gauge theories. We find a phenomenon in the Landau-Ginzburg phase which may enable one to understand which Calabi-Yau σ-models evade destabilization by worldsheet instantons. Examples of (0,2) LandauGinzburg vacua are analyzed in detail, and several novel features ...

________________________ ________________________ UPERIEURE S ORMALE N ECOLE Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity A. AFTALION Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity A. AFTALION Abstract The bifurcation of asymmetric superconducting solutio...

In the Ginzburg-Landau model for superconductivity a large Ginzburg-Landau parameter κ corresponds to the formation of tight, stable vortices. These vortices are located where an applied magnetic field pierces the superconducting bulk, and each vortex induces a quantized supercurrent about the vortex. The energy of large-κ solutions blows up near each vortex which brings about difficulties in a...