Extremal combinatorics in random graphs and hypergraphs

In this talk, we present recent progress on Tur\'an-type problems in random graphs and hypergraphs. Further, we will examine how these problems connect to the study of large cuts in random graphs, and introduce a tool that allows one to establish the existence of typical properties across all large cuts, simultaneously.

This is joint work with Wojciech Samotij and Maksim Zhukovskii.