Scientific revolutions occur in not one but two phases: first, the demise of a paradigm (see Thomas Kuhn's The Structure of Scientific Revolutions) and second, removing unexamined assumptions that had propped it up. The Copernican revolution abolished geocentricity but not circularity: it remained incomplete until Kepler. The lesser but instructive revolution in the materials sciences sparked by the discovery of aperiodic crystals follows that pattern: periodicity is gone, and we are clearing out its props. My talk will consider three challenges in modeling aperiodic crystals:
The foundations are in my 2013 Mathematical Intelligencer article with Jean Taylor, who gave the independent-but-coordinated Part I on real materials in this seminar on November 10.