|GEOMETRY AND MATERIALS SEMINAR|
|Topic:||Conic Sections, Lorentz Covariance, and Smectic Liquid Crystals|
|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.