Speaker
Description
Liquid crystals provide remarkable examples of two-way coupling between internal order and geometry: orientational or layered order responds to confinement and interfaces, while the resulting elastic stresses can reshape the domain itself. I will discuss recent variational and computational work on this coupling in nematic and smectic systems. In nematic droplets, simultaneous optimization of the director field and interface predicts tactoid shapes and unusual defect-induced geometries, including a symmetry-breaking instability in which reorganization of the orientational field selects a new free-boundary shape. I will also describe emerging work on smectic liquid crystals, where the constraint of nearly equally spaced layers introduces much stronger geometric frustration and gives rise to focal-conic and cusped structures. These examples provide a passive setting in which to understand how order, defects and boundaries select one another, and suggest geometric mechanisms that remain relevant when nonequilibrium stresses and activity are introduced.