This summer, the Department of Mathematics is running an online Special Colloquium Lecture Series on mathematical analysis and applications in allied fields. This lecture series is presented in conjunction with UTC’s NSF-funded Math REU Site. The second lecture will be given next Wednesday, June 29th by Dr. Simion Filip, University of Chicago. I have included the details of Dr. Filip’s lecture below. Undergraduate and graduate students who are interested in Analysis, Algebra, and Number Theory are especially encouraged to attend.
Date: Wednesday, June 29, 2022
Time: 1:00 p.m.-2:00 p.m. (EDT)
Zoom link: https://tennessee.zoom.us/j/92054334179
Title: Riemann’s “Other” Function
Abstract: I will discuss a function introduced by Riemann (less famous than his zeta function) that he defined as $f(x) = \sum sin(n^2x) / n^2$ and suggested to Weierstrass that it is not differentiable anywhere. It was a remarkably prescient construction, and while it turns out that Riemann’s function is differentiable at some of the rational points, it also gives an example of a “multifractal” function exhibiting rich behavior at different scales.
I will explain what that means mathematically and provide the necessary background in Fourier analysis, discrete subgroups of Lie groups, dynamics on homogeneous spaces, and how all these notions are related to Riemann’s function and shed light on its behavior.