Dhruv Mubayi: The Feasible region of hypergraphs

Abstract:
Many extremal hypergraph problems seek to maximize the number of edges  subject to some local constraints. We aim to gain a more detailed understanding of such problems by studying the maximum subject to an additional global constraint, namely the size of the shadow.  Put differently, we seek the pairs (x,y) in the unit square such that there are F-free hypergraphs whose shadow density approaches x and edge density approaches y. I will give some general results about the shape of this "feasible region" and also extend and improve some classical Turan-type results for particular choices of F.  This is joint work with Xizhi Liu.

https://zoom.us/j/2961946869