Description
A small perturbation of the maximal stable state in sandpile models on big subsets of the standard grid exhibits tropical curves. A proof of the planar case uses certain dynamics on tropical curves, while curves appearing in this dynamic are smooth or nodal. A direct generalisation of the problem for higher dimensions leads to tropical hypersurfaces which have only mild singularities. This means that the dual lattice polyhedron for each face (of any dimension) of such a hypersurface contains no lattice points except vertices. I explain the motivation from sandpiles and give an overview of the aforementioned dynamics.
