The GreenTao theorem for number fields
 Date
 March 22 at 16:00  18:10, 2021 (JST)
 Speaker

 Dr. Wataru Kai (Assistant professor, Mathematical Institute, Tohoku University)
 Venue
 via Zoom
 Language
 English
5, 11, 17, 23, 29 are prime numbers which form an arithmetic progression of length 5. A famous theorem of Ben Green and Terence Tao in 2008 says there are arbitrarily long arithmetic progressions of prime numbers. Algebraic number theorists are also interested in more general numbers like square roots of integers. Recently, Mimura, Munemasa, Seki, Yoshino and I have established a generalization of the GreenTao theorem in such a direction.
In the first 50 minutes of my talk, I would like to explain some background and technology behind the GreenTao theorem. In the second half after a break, I explain the concept of number fields to formulate our generalization of their result. I will also discuss how one of the new difficulties, which I call the norm vs length conflict, is handled by a technique called Geometry of Numbers.
*Please contact Keita Mikami or Hiroyasu Miyazaki's mailing address to get access to the Zoom meeting room.