侯建锋，福州大学教授

A cut of a hypergraph is a partition of its vertex set into two parts, and the size of the cut is the number of edges which have nonempty intersection with each of the two parts. A classical result of Shearer asserts that every triangle-free graph has a large cut in terms of its degree sequence. This is further generalized to graphs with sparse neighbourhoods by Alon, Krivelevich and Sudakov. In this talk, we study analogues of this and related results in 3-uniform hypergraphs with sparse neighbourhoods, improving some recent results of Conlon, Fox, Kwan and Sudakov.