Tropical Solutions to Hard Problems in Auction Theory

Explore the fascinating world of tropical mathematics in this 51-minute lecture, the fourth in a series by Ngoc Mai Tran. Delve into the min-plus (or max-plus) algebra and discover how tropical objects serve as limits of classical ones while exhibiting polyhedral geometry. Learn how these powerful concepts have been applied to solve diverse problems over the past decade, ranging from deep neural networks and semigroups theory to auction theory and extreme value statistics. Examine key topics such as polytopes, algorithms, the Abappa identity, tropical additive identity, semigroup matrices, bicyclic identities, and random staircase paths. Gain insights into the practical applications of tropical mathematics and its potential to revolutionize various fields of study.