Jinhae Park Chungnam National University Since the Landau-de Gennes theory for Liquid Crystals can explain many phenomena observed in the literature that cannot be captured by the classical Oseen-Frank energy, a great deal of works related to the theory have been recently done by many scientists. The theory gives rise to many interesting mathematical questions including interface problems between different liquid crystal phases. In this talk, we shall discuss some mathematical results and questions on interface problems.