On the study of singularities of mathematical models for liquid crystals

Lia Bronsard
Department of Mathematics and Statistics, McMaster University, Hamilton

The mathematical analysis of liquid crystal models is difficult, as can be seen by their close relationship to the study of singularities for harmonic maps. In this talk, I will present several mathematical models used to study liquid crystals, as well as the connection with classical results on harmonic maps. I will then present new results on energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle in the context of the Landau de-Gennes energy. The Landau de-Gennes model allows for a greater variety of singularities than is allowed in the Oseen-Frank model, which is related to harmonic maps with values in the unit sphere.