Project A3: Codes and designs
In Project A3, the representation theory of finite Weyl groups interacts with harmonic analysis and algebraic combinatorics. Here, the goal is to investigate packings and designs in various settings. The ambient spaces of particular interest for the project are Grassmannians and Stiefel manifolds, as well as association schemes arising from finite classical polar spaces and from finite groups, especially finite reflection groups. In the latter case, essential use of representation theory will be necessary to establish the existence of asymptotically optimal designs, whereas for polar spaces and manifolds, methods of harmonic analysis, such as addition theorems for multivariate special functions, will be crucial.