From Fourier’s cellar to modern harmonic analysis
Organizers
Speaker
Time
Monday, March 23, 2026 2:35 PM - 3:15 PM
Venue
A6-101
Online
Zoom 388 528 9728
(BIMSA)
Abstract
Beginning with Fourier's work on the heat equation and trigonometric expansions, and continuing through the contributions of Dirichlet, Riemann, Lebesgue, Calderón, Zygmund, Carleson, Stein, and many others, Fourier analysis has developed over more than two centuries into one of the central languages of modern analysis. This talk is intended as a guided journey through some of its main ideas. Taking Fourier's classical model of the cellar as a point of departure, I will explain how heat flow leads naturally to semigroup methods, how questions of local regularity and directional behavior lead to singular integrals and Riesz transforms, and why maximal operators occupy a central place in the subject. I will then briefly indicate how the same perspective extends to the Ornstein-Uhlenbeck semigroup and Gaussian harmonic analysis. The emphasis will be on the conceptual unity of the subject rather than on technical details.
Speaker Intro
Mahdi Hormozi is an Assistant Professor at BIMSA working in harmonic analysis, with a focus on Fourier analysis, singular integrals, and related questions in operator theory and PDE.