Seminar on Banach and Metric Space Geometry

Date: September 30, 2016

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Gilles Pisier, Texas A&M

Title: Sidon sets in duals of compact groups and generalizations

Abstract: We will recall some of the classical theory of Sidon sets of characters on compact groups (Abelian or not). In particular we discuss Sidon sets of integers in ℤ and Fourier series on the unit circle, which is the main Abelian case. We will then give several recent extensions to Sidon sets, randomly Sidon sets and subgaussian sequences in bounded orthonormal systems, following recent work by Bourgain and Lewko, and by the author, both currently available on arxiv. The second lecture will focus on the non-commutative case, i.e. sets of irreducible representations on compact (a priori non-Abelian) groups. The case of matricial systems, analogous to Fourier-Peter-Weyl series on compact groups, connects the subject to random matrix theory. An unpublished result of Rider (circa 1975) will also be highlighted. The case of matricial systems, analogous to Fourier-Peter-Weyl series on compact groups, connects the subject to random matrix theory. An unpublished result of Rider (circa 1975) will also be highlighted.