Circles and Primes and Squares Oh My!

Date:

A Presentation for the Postgraduate Seminar Series on the Gauss circle problem and counting the number of integer solutions to the equation $x^2 + y^2 = n^2$.

Abstract

Have you ever wondered exactly how many integer lattice points are contained in a circle centered at the origin of a given radius? Or have you pondered if it is possible to find pi from counting primes? Are the integers getting a bit boring for you and you’re looking for a cool new number system that relates circles and the complex plane in an exciting new way? Then this is the talk for you! Spend an hour (45 minutes) with me as we discover not one, not two, but three ways to solve Gauss’ circle problem and learn a few of the classic themes and concepts within Number theory as we go.