Patrice Ossona de Mendez: Compactness of the Graphon Space and Szemerédi Regularity Lemma

Graphons are analytics objects --- symmetric measurable functions from [0,1]× [0,1] to [0,1] --- which have been introduced by Lovasz and Szegedy to represent limits of (left) convergent sequences of graphs. The space of graphons, endowed with the cut distance $delta_\boxempty$, forms a compact space (as proved by Lovasz and Szegedy). The topic of this talk is to show how Szemeredi regularity lemma can be derived from this compactness result.