Seminar

We will recall some of the classical theory of Sidon sets of characters on compact groups (Abelian or not), and its connections with Gaussian random variables. We will then give several recent extensions of the notions of Sidon set, randomly Sidon set and subgaussian sequence in bounded orthonormal systems, triggered by Bourgain and Lewko’s recent work. In the second part of the talk, non-commutative analogues will be discussed, involving Sidon subsets in the dual of compact non-Abelian groups. The case of matricial systems, analogous to Fourier-Peter-Weyl series on compact groups, connects the subject to Random Matrix Theory. Several open problems will be discussed. All relevant papers are currently available on arxiv.