Fourier analysis: from heat transport to quantum applications

Over 200 years ago, in the throes of the French Revolution, Joseph Fourier had the brilliant insight that any function could be decomposed as a sum of sines and cosines. Despite its importance for mathematics, this result has its roots in the physical problem of heat transport. I will discuss selected applications of Fourier analysis which illustrate its significance in physics. Starting with the historical solution of the heat equation, I will go on to show how the Fourier transform enters scattering problems, and explain how this connects with quantum algorithms. I will conclude with an outlook on current research on quantum many-body interference, where Fourier analysis also plays a role.