Abstract: 

Szemerédi's regularity lemma is a fundamental result in graph combinatorics. But the bound can be unavoidably large for general (hyper)graphs. On the other hand, the result can be viewed as results about hypergraphs with the edge relation definable. When its first-order theory satisfies some tameness condition in model theory, we can get better bound for the result. This is an expository talk on the paper `the definable regularity lemmas for NIP hypergraphs' by Artem Chernikov and Sergei Starchenko.