Abstract: This talk is meant to be an introduction p-adic number and p-adic analysis. These arise via completing the rational numbers using a metric (relative to a prime number p) which is very different from the ordinary euclidean metric. The first part of the talk will introduce this number system and focus on ways in which it differs from our "Euclidean" intuition. We then will discuss p-adic integration. We will then define the p-adic zeta function. The goal will be to describe (without proof) how these are related to the Riemann zeta function. This talk is aimed at 1st year graduate students.
