This mini-course will cover a range of topics related to random minimum spanning trees and, to a lesser extent, uniform spanning trees. It is possible the below lecture plan will be adjusted, either to cover necessary background material, or as a function of the interests of the audience.

- Day 2: UST local structure. Galton-Watson processes, infinite spines. Percolation phase transitions. Giant components, small components. Kruskal-minimum spanning forest coupling.