Dive into the fascinating world of extremal set theory in this comprehensive seminar presented by Andrey Kupavskii, a member of the School of Mathematics at the Institute for Advanced Study. Explore key concepts such as shifting, shifting families, partial order, and the intriguing Katniss Theorem. Gain insights into binomial coefficients, shadow minimization, and order analysis. Follow along as Kupavskii breaks down complex proofs through case analysis and induction, ultimately leading to a deeper understanding of threshold concepts in discrete mathematics and computer science.