액정의 수학적 이론인 란다우-드젠 에너지의 평형해가 만족하는 편미분방정식의 다양한 성질들을 연구한다. 특히, 평형해에서 나타나는 특이점(singularities)을 비선형 해석(변분론)과 편미분방정식 이론들을 이용하여 연구하고 수치해석학 및 신경망 이론을 이용하여 근사해를 분석한다.

Research interests in our lab are mainly focused on calculus of variations, partial differential equations, nonlinear functional analysis and bifurcation theories together with numerical analysis of problems arising in materials science and condensed matter physics. In particular, we investigate various properties of nonlinear partial differential equations which correspond to equilibrium states of the energies for systems of liquid crystals. Currently, we are working on Landau-de Gennes theory for liquid crystals and Neural Networks for Data Analysis.