Artem Chernikov

UCLA

## Time:

Monday, November 4, 2019 - 4:00pm

## Location:

RH 440R

Fix an arbitrary bipartite finite graph H, and let's consider the family of all finite graphs not containing H as an induced subgraph. Recently a strong form of Szemeredi's regularity lemma for such families was established by Lovasz and Szegedy. In particular, up to an arbitrary small error, such graphs can be uniformly approximated by direct products of unary relations. Using a combination of analytic, combinatorial and model-theoretic methods, we establish a generalization of this result for hypergraphs, showing that k-ary hypergraphs omitting a fixed k-partite hypergraph can be uniformly approximated by relations of arity smaller than k. No prior knowledge of the aforementioned notions will be assumed. Joint work with Henry Towsner.