Fairest edge usage in spanning trees
This talk will explore several interesting and interrelated optimization problems involving the spanning trees of a graph. Each problem will be connected to a single fundamental question: How should we choose a probability distribution on the spanning trees of a graph that treats the graph's edges as "fairly" as possible? Along the way, we'll talk about random spanning trees, modulus, effective resistance, minimal spanning trees, densest subgraphs, minimum feasible partitions, and the solution of a secure network broadcast game.