MPHA Seminar, Blocker 627, 30th November 2007, 1:50pm

Speaker: Maxim Zyskin, UT Brownsville
Title: Liquid crystals in polyhedral domains

Liquid crystal configurations in polyhedra with tangent boundary conditions can
be described by maps from a contractible polyhedra to a sphere, which maps faces
of polyhedra to great circles of the sphere. Homotopy classification of such maps
can be given in terms of certain homotopy invariants. Stable configuration of
liquid crystal are harmonic maps corresponding to local minima of Dirichlet
energy functional. We discuss lower/upper bounds for infimum energy for such maps
in a fixed homotopy class. Lower bounds can be given in terms of certain lengths
of minimal connections, but in some cases that can be improved. This work has
applications to new type of liquid crystal displays.