Patterns in thin elastic sheets

The old field of thin-sheet elasticity, dating back to Euler, has had a
remarkable revival in recent years. One of the main reasons has been the
inadequacy of traditional perturbative approaches to account for patterns
observed in ultra-thin sheets. We will review the recent developments and
then focus on an exemplary problem -- a fluid-supported sheet under
compression -- which exhibits periodic ("wrinkled") and localized
("folded") patterns. This system is integrable and reveals a new and
unexpected symmetry.