Explore a 54-minute lecture on Vergleichsstellensätze for ordered semirings, presented by Tobias Fritz at the Centre de recherches mathématiques (CRM) Workshop on Tensors: Quantum Information, Complexity and Combinatorics. Delve into the semiring structure of tensors and resource theories in quantum information, focusing on two theorems that strengthen Strassen's separation theorem by weakening its Archimedeanicity assumption. Discover how these "Vergleichsstellensätze" provide criteria for asymptotic and catalytic resource convertibility, and examine their applications in random walks, SU(n) representation theory, and matrix majorization. Learn how these theorems make asymptotic and catalytic orderings computable and offer simple formulas for asymptotic conversion rates. The lecture covers topics such as majorization between probability distributions, Nielsen's theorem, homomorphisms, and generalizations of the main concepts.