MATHEMATICS COLLOQUIUM

 WHEN:
On Friday, February 22, 2002 at 2.30PM

WHERE:
Durham Science Center, Room 255

WHAT:

Ryan Karr
University of Nebraska - Lincoln

will give a talk on

Abstract:
Pell's equation has the form XX - NYY = 1, where N is a positive integer. Indian mathematicians of the 11th century (!) had an algorithm for finding ALL integer solutions X and Y to such an equation. We will begin by looking at this algorithm. Next, we will connect Pell's equation to some important ideas in modern algebraic geometry (nothing too technical, I promise). Finally, (if time permits us) we'll take a quick glance at how Arakelov theory unites these ancient and modern views of Pell's equation.