Ahmed Bou-Rabee

The Abelian sandpile growth model has a fascinating fractal structure. I will give an overview of what we know on deterministic and random lattices and discuss several open questions. There are connections to circle packings, rational approximation...

I will describe the large-scale behavior of a random growth model (Internal DLA) on random planar maps which approximate a random fractal surface embedded in the plane (Liouville quantum gravity, LQG). No prior knowledge of these objects will be...