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The Ginzburg-Landau energy and its mathematical study, started in the foundational work of Béthuel-Brezis-Hélein, is inspired by superconductivity. The phenomena observed in liquid crystals suggest new questions as well as modifications of the Ginzburg-Landau energy. I will be presenting results on defects in case of tangential boundary conditions and in case we add a divergence or curl penalization term.