Originating in the pioneering work of J. L. Taylor on noncommutative spectral theory, free noncommutative functions theory can be viewed as a theory of - classical - functions defined on operator spaces. Since an operator space is a family of matrices over a base space, some natural compatibility conditions are imposed on functions defined on operator spaces. It turns out that already from these conditions alone, surprisingly many interesting properties can be deduced. These properties made various versions of noncommutative functions into very powerful tools which found applications in an impressive array of other mathematical fields. Among them one can mention operator algebras and operator spaces, noncommutative, and especially free, probability, random matrix theory, systems and control theory, the theory of automata and formal languages, as well as problems in quantum information theory, and the noncommutative moment problem.  On the other hand, free noncommutative functions are objects of interest in their own rights: numerous results from classical functions were recently extended to their noncommutative counterparts.

Our program touches upon both theoretical and applied aspects of free noncommutative functions. In the first workshop of the program, we consider mainly the new developments of the abstract theory of free noncommutative functions, while the second workshop focuses primarily on applications to free probability and random matrix theory originating in Voiculescu's work.

Graduate students please note the deadline to apply for funding is MAY 27th.

Celebration Banquet

In the evening of Friday, June 14th, there will be a banquet celebrating (to the day!) the 70th birthday of Dan Voiculescu.
- The dinner is at Bodega Restaurant - 30 Baldwin St - Cash bar at 6 pm, dinner at 6:30 pm -