July 10 (Mon) at 13:30 - 14:30, 2017 (JST)

The goal of number theory is to reveal the mystery of natural numbers 1,2,3…. It has a long history, and it is still developing by exchanging ideas with many other branches of mathematics. In the long history, number theory had been thought of as a pure mathematics with no direct application outside mathematics. However, the rapid development of computer science changed the situation: the theory of prime numbers has been applied to code theory, cryptography, random number generation etc. It seems that there are several researches in physics and biology using the method of number theory, too.

The aim of this talk is to give a beginner-friendly introduction to number theory. Among many topics, I will focus on very fundamental and important concepts: the “p-adic numbers” and the “finite fields.” I hope that this talk will motivate you to relate your research to number theory.