Restricted Extremal Problems in Hypergraphs
Explore the intricacies of extremal problems in 3-uniform hypergraphs in this 47-minute lecture by Mathias Schacht. Delve into the challenges of determining the maximum cardinality of 3-element subsets within a given set, a problem that has remained unsolved for eight decades. Examine a variant of this problem that imposes additional restrictions based on quasirandom hypergraph theory, leading to more manageable subproblems. Learn about the unifying framework for these problems, including those studied by Erdos and Sós in the 1980s. Discover recent progress in the field, covering topics such as Turán's problem, uniformly dense graphs, Szemerédi's regularity lemma, and hypergraphs with uniformly dense links. Gain insights into this complex area of mathematics through detailed explanations and accompanying presentation slides.