This workshop intends to deepen existing connections and establish new ones between quantum harmonic analysis, the theory of Toeplitz operators on Bargmann-Fock spaces and Bergman spaces, mathematical physics, quantum information, machine learning, and time-frequency analysis.

Background summary: 

Quantum harmonic analysis emerged from the article Quantum harmonic analysis in phase space, J. Math. Phys., 25(5):1404–1411, 1984 by R. F. Werner. The theory is based on the key insight that the analogs of Wiener’s approximation theorem for L-p spaces hold for certain operators (Schatten class operators). For the theory to work, the following extensions of classical concepts for functions are needed:
(1) Banach spaces for operators
(2) A translation for operators
(3) A convolution for operators
(4) A Fourier transform for operators
These concepts shall be re-called in introductory lectures.