Peter Allen: Tight cycles and regular slices in dense hypergraphs

We describe a general approach to the strong hypergraph regularity lemma, which we call 'regular slices', which avoids many of the usual technical complications and retains the features one would like to use in extremal hypergraph theory. This talk will avoid painful technical details in so far as that is possible and focus on an application, proving a hypergraph extension of the Erdos-Gallai theorem.

This is joint work with Julia Boettcher, Oliver Cooley and Richard Mycroft.