Event date:
Sep 6 2021 6:00 pm

Fourier meets Riemann: Some Problems on the Interface between Analysis and Number Theory

Professor Emanuel Carneiro
The field of harmonic analysis aims to understand, qualitatively and quantitatively, he several types of oscillatory phenomena in nature. The Fourier transform (après the work of Jean-Baptiste Joseph Fourier 1768-1830) is one of the main mathematical tools we have for that. The field of analytic number theory, as the name suggests, uses tools from analysis to understand different types of problems in number theory. One of the central objects therein is the Riemann zeta-function, a beautiful bridge between the prime numbers and complex analysis, presented in the celebrated work of Bernhard Riemann in November 1859. In this work, Riemann proposes what would later become, for many, the Holy grail of modern mathematics: the Riemann hypothesis. Having lived from 1826 to 1866, Riemann probably never met Fourier in person, and in this lecture Dr. Carneiro will speculate a bit around some themes they could talk about, i.e., some problems that lie on the interface between harmonic analysis and analytic number theory. And of course, tell a story or two about the Riemann hypothesis, on the occasion of its 162nd birthday this coming November 2021. The lecture will be aimed at a broad audience, with only a minimal background analysis.

Professor Emanuel Carneiro (ICTP, Italy) will be speaking about “Fourier meets Riemann: Some Problems on the Interface between Analysis and Number Theory” in the next John Conway Spirited Seminar Series on September 6th, 2021, at 6pm PST. The seminar is organized by the Department of Mathematics at SBASSE LUMS.

Individuals interested in being part of the seminar can join via Zoom Meeting ID: 97379855766