MLC

Abstract

After the seminal contributions of A. Turing, G.I. Taylor, L. Landau, L. Michel in the first half of the past century, new mathematical methods have emerged to study the phenomenon of spontaneous pattern formation. Decisive progress was made using geometrical methods (M. Golubitsky, I. Stewart) and analytical tools (G. Iooss, K. Kirchgässner). I shall show on examples how this theory, known as Equivariant Bifurcation Theory, applies to a variety of problems, including liquid crystals. I shall also quote some open questions which are still under investigation by mathematicians working in these topics.