Explore the profound impact of the KKL Theorem in mathematics through this 45-minute lecture by Ehud Friedgut, presented by the International Mathematical Union. Delve into the world of hypercontractivity, graph properties, and isoperimetric inequalities. Examine the Junta theorem and its applications to dictatorship and t-intersecting families. Investigate the Sès-Simonovits conjecture and its resolution. Discover the connections between graph products, traffic lights, and hypergraph theory. Gain insights into the fascinating realm of intersecting families of permutations and their mathematical implications.