Analysis, Dynamics, and Applications seminar: Shankara Narayanan

Abstract: Nematic liquid crystals are described by unordered tangent line fields whose local distortion can be decomposed into splay and bend. I consider a model in which the locally preferred state has zero splay and constant nonzero bend. On the hyperbolic plane, this condition is perfectly compatible with the ambient curvature: the corresponding ideal textures are fields tangent to horocycles. The situation changes when looking at a closed hyperbolic surface which does not allow a global horocyclic texture to descend. Therefore, the local preferred state is globally frustrated.

I will discuss a variational formulation of this obstruction and the question of whether the nematic energy admits a geometric lower bound.