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K-State Today

February 22, 2021

Mathematics Department Women Lecture Feb. 23

Submitted by Reta McDermott

Yu-Ru Liu, University of Waterloo, will present "Diophantine Problems in Function Fields" as part of the Mathematics Department Women Lecture Series in celebration of the 50th anniversary of the Association for Women in Mathematics. The colloquium will take place from 2:30-3:20 p.m. Tuesday, Feb. 23, via YouTube Live.

The abstract for the lecture is: Let $\mathbb{Z}$ be the ring of integers, and 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 prime number $p$, it is an interesting phenomenon in arithmetic that these two rings resemble one another so faithfully. 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 Waring's problem about representations of elements with fixed powers.