Random geometric structures Many models arising from statistical physics, chemistry, biology and computer science have a common mathematical theory. We will start by learning about random walks and their connections to the harmonic measure, harmonic analysis and spectral theory. We will discuss the scaling limit of random walk, called Brownian motion, and its invariance under conformal maps on the complex plain. We will move on to define different geometric processes such as the random first passage percolation metric, diffusion limited aggregation, Eden model and Richardson’s model, and analyze them using tools from probability theory and deep connections to other mathematical disciplines. Prerequisites: Math 411, Math 607.