Speaker
Description
Frame fields are locally-defined configurations on $S^2$ that are invariant with respect to a rotation group (for example, the cubic or tetrahedral group), and they are useful in describing nematic liquid crystals or ordered material with nonstandard symmetries. For example, tetrahedral frame fields can be used to describe certain phases in bent-core nematic liquid crystals. In this talk I will discuss methods for generating these fields using higher order tensors and harmonic map relaxations with specific nonlinear penalty functions. In particular the relaxation procedure reliably generates frame fields on arbitrary Lipschitz domains, except on co-dimension 2 sets. I will also describe how to couple such problems to applied magnetic fields. This is a joint work with Dmitry Golovaty, Matthias Kurzke, and Alberto Montero.
