Résumé
Sharp structures can occur as minimizers of very regular problems. This means symmetry can lead us badly astray and the resultant symmetry breaking may lead to highly counter-intuitive structures. I will illustrate in a discrete example and then some continuous examples. The main soft matter example will be the emergence of faceted shapes as the ground states of liquid-crystalline vesicles and the novel ground states of crystalline order on a 2-sphere.
