Mathematics Junior Colloquium

Speaker: Dustin Cartwright (UTK)

Title: The hardest easiest equations

Abstract: The problem of finding integer or rational solutions to a polynomial equation has been studied since the ancient Greeks. Despite the seeming simplicity of this statement, such problems can be very hard to solve, as evidenced by the famous case of Fermat's last theorem, which resisted many proof for many generations. Despite the seemingly discrete nature of integers and rational numbers, these problems are closely related to the geometry of the solutions of the same equations over the complex numbers.