Curvature Driven Structure in Condensed Matter Order
I will discuss the ordering of various states of matter on curved two-dimensional manifolds and the effect of spatial curvature on the basic structure and distribution of elementary topological defects in such systems. I will focus on phenomena with no analogs in the corresponding flat or planar systems. Spatial curvature can drive the delocalization of disclination (curvature) defects, the unbinding of dislocation defects and the fractionalization of interstitial and vacancy defects. The related mathematical (analysis) problems are the determination of several classes of optimal distributions of points or extended structures on two-dimensional manifolds.