Abstract: Ribbons are elastic bodies that are thin and narrow. Many ribbons in nature, from seed pods to molecular assemblies, have non-trivial internal geometry, making them incompatible with Euclidean space. In many cases, this results in shape transitions between narrow and wide ribbons with the same internal geometry. In this talk, I will show how to model these bodies mathematically, discuss the various phenomena they exhibit (and how they are related to the Gauss–Codazzi equations from surface theory), and present some recent rigorous results via Gamma convergence (+ open questions). There will be pictures, there will be theorems, and hopefully a live experiment. Based on joint work with Sharon, Siéfert and Levin (modelling and experiments) and Mora (mathematics).

Contact: Ian Tobasco