Title: From crystals to Wulff shapes
Abstract: We introduce the crystallization problem and its connection to the
Wulff problem. We focus on the minimization of Heitman-Radin potential energies
for configurations of N particles. Besides identifying the asymptotic Wulff
shapes through Gamma-convergence, we introduce the concept of fluctuation and
discuss optimal fluctuations for quasiminimizers proving in particular the
well-known N^{3/4} conjecture for minimizers on planar lattices. Our technique
combines the sharp quantitative Wulff inequality with a notion of quantitative
closeness between discrete and continuum problems. We eventually discuss some
recent result on the three dimensional case obtained in collaboration with Gian
Paolo Leonardi (Trento) and Leonard Kreuz (Münster).