Folding, Crumpling, and Coloring: A Spin Model with Geometric Constraints

Emily Russell (ICERM)

Abstract :

I am interested in the mechanics of two-dimensional membrane materials, and in particular in how they bend and fold. A simplified 2D folding problem has a classical expression as a 2D Ising spin model, modified by local geometric constraints. This is also known to have an interpretation as a 3-coloring problem on the lattice, which was previously exactly solved by Baxter in the 70s.

I will introduce some of the classical results on membrane mechanics from physics, and develop the corresponding mathematical problem and sketch the geometric elements of its solution. If time permits, I will also discuss the extension to a 3D folding problem.