Alexander Wang, University of Washington

PDL C401
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 padic 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 padics, 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