Several topics in complex phases of condensed matter will be studied. The revision of classical crystallography necessitated by the discovery of icosahedral quasicrystals will be extended and completed, in parallel with efforts to extend two- and three- dimensional tiling theory to provide templates for the new non- crystallographic space groups. A new numerical approach to the computation of the equilibrium blue phases of chiral nematics will be explored, based on the exact solutions of the infinite chirality limit down to physical values of the chirality.
