Mathematical Conversations

Gaussian periods are certain sums of roots of unity.  Gauss introduced them in his work on straight edge and compass constructions of regular polygons.  Since then, Gaussian periods have played important roles in number theory and beyond.  It turns out that Gaussian periods also have striking visual properties!  This talk will explore the following question: What happens when you plot really large families of Gaussian periods in the complex plane?  About a decade ago, an undergraduate named Bob Lutz asked this question and opened the door to a surprisingly rich collection of illustrations.  This talk will be accessible to anyone with an undergraduate background in abstract algebra.  If you like nice pictures and surprising, new views on old subjects, this talk is for you.  If you can’t wait and want to start exploring before the talk (or alongside it), check out this app for Apple computers: https://apps.apple.com/us/app/gaussianperiods/id1622050577