Undergraduate Seminar: "Counting number fields: problems and progress"

Abstract: Arithmetic statistics is a flavor of number theory focused on counting mathematical objects or studying their distribution. These objects of interest could be almost anything, but some popular choices are prime numbers, points on curves, and field extensions. In this talk we will focus on the latter, giving an overview of some of the many fascinating results and conjectures on the distribution of number fields--finite field extensions of the rational numbers. We'll discuss the famous cases of number fields of degree up to 5, explore the best currently known results in the general case, and visit a frontier of active research: counting fields generated by points on an algebraic curve.

Host: Adeli Hutton