Abstract:
Non-Euclidean elasticity is both a physical theory and a source of many natural geometric questions. Physically, it is a framework for understanding the shapes of leaves, molecular structures, and other systems with inhomogeneous growth. Mathematically, it asks how manifolds can be immersed in Euclidean space “as isometrically as possible,” leading to questions about the structure of spaces of isometric immersions, their stability, and related variational problems.
In this talk, I will introduce the model through several examples, including shape transitions in molecular structures and the ways singularities in isometric immersions of hyperbolic metrics shape kale leaves. Along the way, I will discuss some of the mathematical questions that arise — some resolved, many still open.
There will be pictures, there will be theorems, and, hopefully, even a live experiment.
