Conic Sections, Lorentz Covariance, and Smectic Liquid Crystals

GEOMETRY AND MATERIALS SEMINAR
Topic:Conic Sections, Lorentz Covariance, and Smectic Liquid Crystals
Speaker:Randy Kamien
Affiliation:University of Pennsylvania and Member, School of Mathematics
Date:Monday, May 24
Time/Room:3:30pm - 4:30pm/S-101

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. We have developed an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including Apollonian packings, the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.