Ecole d’été régionale franco-roumaine en mathématiques appliquées, Sinaia, 2 - 11 Juillet 2017
Introduction aux Mathématiques des cristaux liquides
Arghir Dani Zărnescu - Basque Center for Applied Mathematics, Bilbao &
“Simion Stoilow” Institute of Mathematics of the Romanian Academy
Liquid crystals are a surprising material, sometimes referred to as "the
fourth state of matter" (after solid, liquid and gas). Despite their
impressive technological applications in the last decades, their understanding
at a fundamental level is still modest and there exist several major theories
that compete in proposing a mathematical model efficient in describing them.
The course will focus on the Q-tensor model, proposed by Pierre Gilles de
Gennes in the 70s and an important reason for awarding him a Nobel prize in
physics in 1991.
We shall study aspects related to the theory of partial derivatives equations,
as well as interactions with linear algebra, topology and geometry. These
interactions motivate the mathematical fascination associated to the study of
liquid crystal models, as well as being the main source of mathematical
challenges generated by this model
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