(This colloquium has been canceled.)

Since the development and commercialization of the first nematic liquid crystal display devices in the middle of the last century, mathematical modeling and analysis of liquid crystals has experienced significant progress. Liquid crystals are phases intermediate between solid and liquid; they occur in synthetic as well as in organic compounds. The Kevlar fiber is an example of a highly employed liquid crystal polymer; many virus and bacteria colonies as well as biological tissues present liquid crystal ordering.

Liquid crystals of small molecular weight consist of rigid, rod-like molecules that tend to follow preferential directions of alignment. Their interaction with electric and magnetic fields is at the core of application to display devices. Recently developed liquid crystals exhibit more complicated molecular shapes able to sustain permanent dipoles that result in ferroelectric coupling with applied electromagnetic fields. The speed of switching of such devices is about 10^3 to 10^4 times that of the nematic cell. Equilibrium states of ferroelectric liquid crystals result from minimizing the total energy subject to packing and electrostatic constraints. I will present an application of such a theory to predicting shape of material filaments.

Liquid crystal elastomers are nonlinear elastic solids that may also present liquid crystal phases. One remarkable feature is their capability to undergo unusually large deformations along preferential directions. Upon analyzing mathematical issues of such models, I will address their gel states and discuss the potential matrix role in modeling cell motility in the brain.