唐与聪，南京航空航天大学

Hypergraph regularity lemmas are generalizations of Szemerédi's regularity lemma for graphs, which has been proved to be a powerful tool with many subsequent. In this talk, we first give a brief introduction to Szemerédi's regularity lemma for graphs and associate lemmas. Then, we give the definitions of regular complex, which is the basic object in the hypergraph regularity lemmas. Finally, we give several useful lemmas depending on regular complex.