Extremal combinatorics and the Frankl-Füredi conjecture
Natasha Morrison (Cambridge and IMPA)

In this talk, we explore the origins of hypergraph Lagrangians and some of their applications to classical problems in extremal combinatorics. We then focus on the Frankl-Füredi conjecture, which concerns the maximal  value of the Lagrangian of an r-uniform hypergraph with a fixed number of edges. In particular, we show that the conjecture is false in general, but holds for all sufficiently large $3$-uniform hypergraphs. [Based on joint work with Vytautas Gruslys (Cambridge) and Shoham Letzter (ETH Zürich).]