Title:  The Beauty of the Kaczmarz Algorithm.

Abstract: Stefan Kaczmarz introduced a method for solving systems of linear equations in 1939 that now bears his name. Remarkably, his idea was quite elementary and yet quite profound. The Kaczmarz algorithm has appeared in numerous contexts, including computerized tomography, optimization, data science, as well as harmonic analysis and operator theory. We'll discuss some of the history of the method in various guises as well as my own interest in its application to answer questions about the existence and construction of Fourier series expansions.