On November 19, we invited Professor Shin-ichiro Seki from Aoyama Gakuin University to give a talk in the Math Seminar. He explained about the graph removal lemma, which is one of the key ingredients of the proof of his recent joint work with Kai, Mimura, Munemasa and Yoshino on a generalization of the celebrated Green-Tao theorem. In the first half of the talk, he gave a survey of Szemerédi's regularity lemma and the graph removal lemma, and explained how to extend the removal lemma to the case of (weighted) hypergraphs. In the second half of the talk, he presented Fox's result on a quantitative version of the graph removal, and discussed the prospects for future research. After the seminar, we had an online drinking party, and enjoyed a lot of discussion with the speaker.

Reported by Hiroyasu Miyazaki