Mathematical problems in liquid crystals

Research Group Zarnescu

August 15 - September 15, 2011 and June 1 - July 31, 2012

Organizers: Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu

This program brought together young analysts conducting research in variational models for liquid crystals to make a significant progress in several challenging open problems. The proposed research aimed to investigate liquid-crystalline systems that are described by Landau-De Gennes Q-tensor theory. The research group was particularly interested in understanding singularities, defects and phase transitions in these systems. For that the group employed methods developed for harmonic maps theory and Ginzburg-Landau theory of superconductivity, and extended them to their setting. The study reduced a widening gap between numerical simulations and analytical understanding of liquid crystalline systems. It also helped to develop new analytical tools for investigation of other physical systems, e.g. polymers, complex fluids.