In the one-month program, the many connections with other fields will appear, but a focus will be provided by emphasizing the distributions of the noncommutative variables. Such variables, like the quantum mechanical observables are operators and the distributions are expectations associated with them. In the case of one variable the noncommutative distributions are expectations of spectral measures and are classical, i.e. probability measures, For several variables such distributions are expectation values of noncommutative monomials (there are many more of these than commutative ones). The program will emphasize in all parts of free probability the distributions aspect: explicit determinations of distributions if possible, methods of computing distributions, uses of facts about distributions in applications. This is a timely topic since recent developments in a variety of directions in free probability are also advances in the distributions aspect, ranging from new noncommutative analysis tools, new combinatorial and discrete mathematics aspects, the appearance of new quantum symmetries and new types of distributions.
July 8 - 18, 2013