The graph removal lemma

We have recently proved an extension of the Green-Tao theorem on arithmetic progressions to number fields, in collaboration with Kai, Mimura, Munemasa and Yoshino. (Kai gave a talk on this result in March.) There are several promising approaches in this area, including ergodic theory and Fourier analysis, but we used a combinatorial tool, the relative hypergraph removal lemma proved by Conlon, Fox and Zhao.

In the first half of this talk, I will give a survey of Szemerédi's regularity lemma and the graph removal lemma, and explain how to extend the removal lemma to the case of (weighted) hypergraphs.
In the second half of this talk, I will present Fox's result on a quantitative version of the graph removal, and discuss the prospects for future research.

*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.