Henry Adams - Fair Division

Explore the fascinating application of Sperner's lemma to solve the problem of fair rent division among roommates with varying preferences. Delve into a 47-minute lecture that examines how combinatorics and topology can be used to equitably distribute rent for an apartment with rooms of differing desirability. Learn about the algorithm behind fair division, including concepts like subdivision, labeling, and rainbow triangles. Discover how this mathematical approach has been featured in a New York Times article and implemented in practical applications. Gain insights into variant forms of Sperner's lemma, its traditional formulation, and algorithmic proof. Engage with thought-provoking questions and real-world scenarios that demonstrate the power of applied algebraic topology in solving everyday fairness problems.