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How do prime numbers decompose?

- Speaker：Assistant Professor Masao OI (Hakubi 10th batch,Graduate School of Science)
- Date：28th January 2020 (Tuesday), 16:30-
- Venue：Conference Room 1&2,The first basement floor, Research Administration Building(Hakubi Center building)
- Presentation Language：English
- Format of the seminar：Closed (only staff of Kyoto University)

Any prime number cannot be decomposed into a product of smaller integers by its definition.

However, this is a story in the world of usual integers.

As every quadratic equation has a solution in the world of complex numbers, in modern mathematics, we often consider a framework which is larger than usual system of numbers and investigate phenomena happening there.

In such a framework, sometimes prime numbers can be decomposed into a product of smaller "integers" (in an extended sense).

In fact, studying such a decomposition of prime numbers in an extended world leads us to so-called the Langlands conjecture, which plays a very important role in modern number theory.

In this seminar, by using several example of phenomena of prime numbers observed by Fermat and Ramanujan, I would like to explain what the Langlands conjecture is and also an approach to this conjecture.