February 22, 2021
Mathematics Department Women Lecture Feb. 23
Yu-Ru Liu, 1xbet online sports betting 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. Thecolloquium will take place from 2:30-3:20 p.m. Tuesday,Feb. 23, via YouTube Live.
The abstract for the lecture is: Let $xbet online sports betting {Z}$ be the ring of integers, and let $xbet online sports betting {F}_p[t]$ be the ring of polynomials in one variable defined over the finite field $xbet online sports betting {F}_p$ of $p$ elements. Since the characteristic of $xbet online sports betting {Z}$ is >130_word_end<$, while that of $xbet online sports betting {F}_p[t]$ 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 $xbet online sports betting {Z}$ and $xbet online sports betting {F}_p[t]$ lies in the field that relates number fields to function fields. In this talk, we will investigate some Diophantine problems in the settings of $xbet online sports betting {Z}$ and $xbet online sports betting {F}_p[t]$, including Waring's problem about representations of elements with fixed powers.