Current research is concerned with the analytical study of physically motivated systems of partial differential equations. So far it has concentrated on several major directions:

• The Q-tensor theory describing liquid crystals
• The Smoluchowski-Doi models describing complex non-Newtonian fluids
• Aspects of classical Newtonian fluids
• The nonlinear Schroedinger equations with potential, used in various applications, in particular in nonlinear optics.

An experiment of Oleg D. Lavrentovich (Kent State University) with defect patterns in nematic liquid crystal sample