Title: Growth Models in the Plane 

 

Abstract:  We'll 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 famous and still very mysterious model is called DLA: it forms the most beautiful fractal patterns (pictures will be provided). Despite this, DLA is actually fairly poorly understood and we will quickly survey the existing ideas (unfortunately there aren't very many).  We will then discuss a new type of growth model that behaves similarly (many more pictures will be shown) and which can be precisely analyzed. No prior knowledge is necessary and there will be lots of pictures and open problems!