Since this is a small event, with friends coming together, I see it as a chance to discuss the state of Fourier Analysis and to dare some predictions, perhaps express some wishes and dreams about the future development of Fourier Analysis. The title should remind about an Album, entitled THE SHAPE OF JAZZ TO COME, which is said to be the starting point of what is now called FREE JAZZ:
https://en.wikipedia.org/wiki/The_Shape_of_Jazz_to_Come
In this sense I will allow myself to wrap up some ideas around terms introduced and developed in the last decase: Banach Gelfand Triples, Postmodern Harmonic Analysis, Computational or Numerical Harmonic Analysis, Conceptual Harmonic Analysis, and various types of possible applications. Of course, the actual presentation will allow only to present phragments and vague ideas, not a complete theory, and thus will necessarily fall short of the great promises potentially arising from the first part of my abstract. Still I will do my best to make it enjoyable, and mix historical with forward looking perspectives, hoping also for inspired discussions after the talk.