Explore the applications of tropical mathematics in solving complex problems across various domains in this lecture by Ngoc Mai Tran. Delve into the power of tropical mathematics, which operates in the min-plus or max-plus algebra, and discover how its key concepts of tropical objects as limits of classical ones and their polyhedral geometry are utilized. Learn about the unimodalization theorem, graphical pricing, competitive pricing, and competitive equilibrium. Examine examples, theorems, and comparative diagrams that illustrate the application of tropical mathematics in deep neural networks, semigroups theory, auction theory, and extreme value statistics over the past decade.