Harmonic analysis in conformal and superconformal field theory

Conformal partial waves are fundamental objects in conformal field theory and their knowledge is a necessary prerequisite for the bootstrap programme. The study of partial waves is naturally a part of harmonic analysis on the conformal group. We take this observation as the starting point and use it to derive various results about partial waves. These include relations of four/higher-point conformal blocks to wavefunctions of Calogero-Moser-Sutherland/Gaudin integrable models and new explicit expressions for superconformal and defect blocks in terms of special functions.