Biaxiality in the Landau-de Gennes model for liquid crystals.

 Nematic liquid crystals are a special phase of matter, somehow intermediate between solid crystals and liquids. Several variational models have been proposed to describe their behaviour. In this talk we focus on the Landau de Gennes model, in a 2-D stationary case. We show that, in the low temperature range, the stable equilibrium configurations are biaxial - that is, the molecules align locally along more preferred directions, at some point. Next, we discuss the asymptotic behavior o f minimizers, as the elastic constant tends to zero, and prove the convergence to a locally harmonic map with singularities.