  We study transformations of self-organized defect arrays at the
nematic-smectic A liquid crystal phase transition, and show that these defect
configurations are correlated, or "remembered", across the phase transition. A
thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an
air interface and a water substrate, and viewed under polarized optical
microscopy. Upon heating from smectic-A to nematic, a packing of focal conic
domains melts into a dense array of boojums---nematic surface defects---which
then coarsens by pair-annihilation. With the aid of Landau-de Gennes numerical
modeling, we elucidate the topological and geometrical rules underlying this
transformation. In the transition from nematic to smectic-A, we show that focal
conic domain packings are organized over large scales in patterns that retain a
geometric memory of the nematic boojum configuration, which can be recovered
with remarkable fidelity.
