SFU Number Theory and Algebraic Geometry Seminar: Shabnam Akhtari

Let $K$ be an algebraic number field. The Primitive Element Theorem implies that the number field $K$ can be generated over the field of rational numbers by a single element of $K$. We call such an element a generator of $K$. A simple and natural question is “What is the smallest generator of a given number field?” (and how to find it!) In order to express this question more precisely, we will introduce some height functions. Then we will discuss some open problems and some recent progress in this area, including a joint project with Jeff Vaaler and Martin Widmer.