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.

Intro
When Erdós forgot to ask the general question
Turan's problem
Turán-type problems for hypergraphs
Prominent open problems
Uniformly dense graphs
Examples of weakly dense hypergraphs cont'd
Szemerédi's regularity lemma
Regularity for 3-uniform hypergraphs
Results and problems for weakly dense hypergraphs
Strengthening the denseness assumption
Hypergraphs with uniformly dense links Definition