Abstract: A thin elastic sheet wrinkles to avoid compression. When the
compression is uniaxial the wrinkling direction is clear, and
the main challenge is to understand its local length scale. When
the compression is biaxial the situation is more complex since
even the direction of the wrinkling is hard to predict. A related
situation occurs when the wrinkling is due to geometric incompatiblity,
for example when a flat sheet is wrapped around a sphere or a curved
shell is flattened by placing it on water. I will introduce this
topic, then discuss several areas of recent progress, including
striking work by Ian Tobasco on wrinkling driven by geometric
incompatibility in a regime involving “asymptotic isometry.”