Dendrites (tree-like crystals) have a profound influence upon the engineering properties of metals, including the material's mechanical, chemical, and electrical responses. The Mullins-Sekerka shape instability provides the fundamental cause for the formation of highly complex, dendritic shapes observed in both natural freezing processes, and in technical applications (casting, welding). Kinetics of melting pivalic acid dendrites was observed under convection-free conditions on the space shuttle Columbia launched in 1997 as STS-87. At low melting Stefan numbers, St

The contractive divisor property for Bergman spaces states
that
given a non-zero square-integrable holomorphic function f on the disc,
there exists a holomorphic function g such that f/g is holomorphic,
nowhere zero, and has square integral no greater than that of f. Recent
work by Aleman, Richter, and McCullough establishes this result via a
reproducing kernel approach. I will discuss the relevant articles.