Title: On ribbons that defy Gauss’s Theorema Egregium: Why some molecules (and other structures) change shape as they grow
Abstract: Ribbons are elastic bodies that are thin and narrow. Many ribbons in nature, from see 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 (+ open questions). There will be pictures, there will be theorems, and hopefully even a live experiment.
Based on joint work with Sharon, Siéfert and Levin (modelling and experiments) and Mora (mathematics).
