Origami, affine maps, and complex dynamics
  We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between NET maps and affine maps makes computation of many invariants tractable. In addition to this, NET maps are quite diverse, exhibiting many different behaviors. We discuss data, findings, and new phenomena. 
William Floyd, Gregory Kelsey, Sarah Koch, Russell Lodge, Walter   Parry, Kevin M. Pilgrim, Edgar Saenz
math.DS