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GT CalVa C ROMAN

Lundi 13 mars 2017

Carlos ROMAN (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie)

3D vortex approximation construction and an application to the study of global minimizers for the Ginzburg-Landau functional below and near the first critical magnetic field

Abstract : The Ginzburg-Landau model is a phenomenological description of superconductivity. An essential feature of type-II superconductors is the presence of quantized vortices, which appear above a certain value of the external magnetic field called the first critical magnetic field. This talk will review some known mathematical tools developed to analyze the vortices, and will provide a new polyhedral approximation of the vorticity in 3D, which allows one to obtain a new lower bound for the energy and a new vorticity estimate. This construction is at the epsilon-level and yields optimal estimates. As an application, we will describe the behavior of global minimizers for the Ginzburg-Landau functional in 3D below and near the first critical magnetic field.