2026 CMS Summer Meeting

Saint John, June 5 - 8, 2026

Krieger-Nelson Prize

YU-RU LIU, University of Waterloo Fermat vs Waring: An Introduction to Number Theory in Function Fields [PDF]: Let $\mathbb{Z}$ be the ring of integers. For a prime number $p$, let $\mathbb{F}_p[t]$ be the ring of polynomials in one variable defined over the finite field $\mathbb{F}_p$ of $p$ elements. Since the characteristic of $\mathbb{Z}$ is $0$, while that of $\mathbb{F}_p[t]$ is the positive number $p$, it is a striking theme in arithmetic that these two rings faithfully resemble each other. The study of the similarity and difference between $\mathbb{Z}$ and $\mathbb{F}_p[t]$ lies in the field that relates number fields to function fields. In this talk, we will investigate some Diophantine problems in the settings of $\mathbb{Z}$ and $\mathbb{F}_p[t]$, including Fermat's last theorem and Waring's problem.