Snapshots on quantum probability

As suggested by the title, the goal of the present talk is to describe some casual photographs of different parts of quantum probability without pretense of completeness. I will choose three topics which, in my opinion, efficiently illustrate the fruitful interplay between mathematics and physics which has characterized the development of quantum probability in the past thirty years: (i) the description of a recent experiment which has brought to a conclusion the long standing debate about possible non local effects as necessary consequences of the basic principles of quantum mechanics; (ii) the notion of interacting Fock space, which emerged from quantum electrodynamics without dipole approximation and turned out to be a fruitful tool in such disparate fields as orthogonal polynomials, asymptotics of graphs, quantum structure of classical probability measures, exclusion statistics, . . . ; (iii) the square (and higher powers) of white noise and its relation to renormalization theory and infinitely divisible processes.