1-2-3 Seminar: Primes, p-adics, and an exploration of local fields

One of the most important aspects of the real numbers is that it is complete: every Cauchy sequence of real numbers converges to a real number. Now that we have the attention of the analysts, we can begin an exploration of other ways to complete the rational numbers! This leads us to the p-adic numbers, a collection of complete fields which are closely related to prime numbers, and allow us to capture arithmetic information in an algebraic way. We'll discuss the structure and properties of the p-adics, some techniques to solve problems over these fields, and how they generalize to a broader class of objects known as local fields.

Zoom Link: https://washington.zoom.us/j/92849568892