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SUMMARY:Yu-Ru Liu (University of Waterloo)
DTSTART:20231025T200000Z
DTEND:20231025T210000Z
DTSTAMP:20260423T035528Z
UID:NTC/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/30/">Fer
 mat vs Waring: an introduction to number theory in function fields</a>\nby
  Yu-Ru Liu (University of Waterloo) as part of Lethbridge number theory an
 d combinatorics seminar\n\nLecture held in University of Lethbridge: M1040
  (Markin Hall).\n\nAbstract\nLet $\\Z$ 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 $\\Z$ is $0$\, while that of $\\mathbb{F}_p[t]$ is the positive prime 
 number $p$\, it is a striking theme in arithmetic that these two rings fai
 thfully resemble each other. The study of the similarity and difference be
 tween $\\Z$ and $\\mathbb{F}_p[t]$ lies in the field that relates number f
 ields to function fields. In this talk\, we will investigate some Diophant
 ine problems in the settings of $\\Z$ and $\\mathbb{F}_p[t]$\, including F
 ermat's Last Theorem and Waring's problem.\n
LOCATION:https://researchseminars.org/talk/NTC/30/
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