# Catch-All Mathematical Colloquium

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### The colloquium will be held once a month. It will be held online for the time being. Each event consists of a one-hour talk on mathematics followed by a one-hour diversity panel discussion session.

In the mathematics part, we will hear an exciting overview talk for a general audience. November speaker is Masato Mimura from Tohoku University. In the discussion session, we will hear about the speaker's experience as a mathematician, especially in choosing fields of research. You can take inspiration from them and exchange ideas with other participants in a small group. After the sessions are over, there will be a tea time where participants can chat freely.

You can join Part I only or both parts of the colloquium. Please register before November 19, 5 pm. Click here to register!

Part I Expository math talk 3-4 pm

Speaker: Masato Mimura 見村万佐人 (Tohoku University 東北大学)

Talk Title : The Green--Tao theorem for number fields

Abstract: The celebrated Green--Tao theorem states that an upper dense subset of the set of rational primes contains arbitrarily long arithmetic progressions. Later, Tao proved that an upper dense subset of the set of Gaussian primes, namely, prime elements in the integer ring $\mathbb{Z}[\sqrt{-1}]$ of the number field $\mathbb{Q}(\sqrt{-1})$ contains arbitrarily shaped constellations. (We will explain the precise statement in the talk.) In the paper, Tao asked whether the same conclusion holds in the setting of arbitrary number fields. In this joint work with Wataru Kai (Tohoku U.), Akihiro Munemasa (Tohoku U.), Shin-ichiro Seki (Aoyama Gakuin U.) and Kiyoto Yoshino (Tohoku U.), we answer Tao's question in the affirmative. We have an application to the setting of a binary quadratic form. More precisely, given a form $F$, we study combinatorics on the set of pair of integers $(x,y)$ for which $F(x,y)$ is a rational prime. No serious background of number theory is required for this talk.

Part II Diversity Panel Discussion 4-5 pm

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