Growth Models in the Plane

We will study the growth of (two-dimensional) things. Think about lichen growing on a tree (tends to be sort of round). Another fun example is electricity propagating through wood (tends to be sort of fractal). A celebrated and rather mysterious model is called DLA: it forms the most beautiful fractal patterns, pictures will be provided. Despite being very well known, DLA is actually fairly poorly understood and we will quickly survey the existing ideas. We will then discuss a new type of growth model that behaves very similarly and which can be analyzed using a different and arguably more elementary set of tools.