Job description

Randomness and random shapes can be found everywhere around us, for example the shape of a tree is influenced by random interactions both between and within its cells, and random external influences. This random growth causes trees in nature to have self-similar, fractal-like properties. Underlying random growth also makes our backyard oak look remarkably similar to other structures in nature and systems of human design, such as the shape of river systems; the circulatory system in animals; and the connectivity structure of the internet and digital social networks. Broccolis looking like trees is a consequence of a universality principle in random structures: the precise random dynamics of cell growth in the two organisms is different, but those differences have a negligible effect on the overall structure.

The goal of this PhD project is to examine universality in random trees and graphs. (Morally, you will rigorously prove what it...