Michael Kiessling, Rutgers University

Abstract

Consider the complete graph whose vertices are the n-th roots of unity in the complex plane. To every edge between a pair of vertices, associate a weight that is a given even non-zero power of the length of the edge. Sum the weights over all pairs of vertices (i.e., over all edges). The result, determined in all generality by Johann Brauchart around 2014 (special cases were known a century before) is always a finite expression in integer powers of n --- thanks to the trivial zeros of Riemann's zeta function. This talk is intended to serve an exciting appetizer to the audience, who hopefully will wish to go for the full meal by reading Johann's papers. Some MAPLE experiments do feature in this talk.

Link to video: https://vimeo.com/680495955

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/