Mathematical analysis of liquid crystalline phase transitions as modeled by Landau-de Gennes type phenomenological energy
functionals, with an emphasis on smectic and bent core molecules liquid crystals. The
intent of the research is to validate and refine theoretical models available in the physics literature.
Specific topics include formation of bulk chevron structures under magnetic field in Smectic A liquid crystals,
switching behaviors of polarization vectors in bent-core liquid crystals and de Vries liquid crystals macroscopic models.
The Ginzburg-Landau theory of superconductivity describes the physical
properties of interest for low temperature superconductors. The study of generalized forms of
the Ginzburg-Landau energy functional, and of the systems which arise using calculus of variations,
presents interesting problems, both from the physical, since there
is an interest in extending such theory to the high temperature superconductors,
and the mathematical, for the difficulties in the analysis of the nonlinear
equations derived, point of views.