Colloquium: Classical Diophantine Equations and Orders in Number Fields

Abstract:  

A number field is a finite field extension of the rational numbers. A central algebraic structure in any number field is its ring of integers. For the ring of integers of a given number field (and any of its subrings), we are interested in exploring whether the ring can be monogenized, that is whether it can be generated by one algebraic integer over the ring of (rational) integers. We will relate this open problem to a family of classical Diophantine equations. The reduction of the problem to the resolution of simple polynomial equations allows us to gain new information about monogenization of rings in number fields with small degrees.

In this talk we will introduce basic concepts from algebraic number theory and explain how some analytic and algorithmic methods can be used to understand some algebraic structures in number fields.

Host: Wanlin Li

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00 - 3:00 pm.