## 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.