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Nonlinear Analysis

Ginzburg-Landau functionals for a general compact vacuum manifold on planar domains

Jean Van Schaftingen, UCLouvain, Louvain-la-Neuve, Belgium

Location:  Room 705
Date & time: Tuesday, 28 January 2020 at 1:40PM - 3:00PM

Abstract: Ginzburg–Landau type functionals provide a relaxation scheme 
to construct
harmonic maps in the presence of topological obstructions. They arise in
superconductivity models, in liquid crystal models (Landau–de Gennes
functional) and in the generation of cross-fields in meshing. For a general
compact manifold target space we describe the asymptotic number, type and
location of singularities that arise in minimizers. We cover in 
particular the
case where the fundamental group of the vacuum manifold in nonabelian and
hence the singularities cannot be characterized univocally as elements 
of the
fundamental group. The results unify the existing theory and cover new
situations and problems.
This is a joint work with Antonin Monteil and Rémy Rodiac (UCLouvain,
Louvain-la-Neuve, Belgium).