Abstract: Topological complexity is a numerical invariant quantifying the difficulty of motion planning in a space. Applied to configuration spaces, it measures the difficulty of collision-free motion planning. In many situations of practical interest, the environment is reasonably modeled as a graph, and the topological complexity of configuration spaces of graphs has received significant attention for this reason. This talk will discuss a proof of a conjecture of Farber, which asserts that this invariant is as large as possible in the stable range. No prior knowledge will be assumed beyond basic algebraic topology.