Objectives
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.
Scientific Activity
Program activities will be around two one-week-workshops (at the
beginning and at the end of July) and, in the 2 weeks between workshops,
seminars and other activities, mostly especially adapted for the
very young (including graduate students and postdocs). The first
workshop will be more on the combinatorics side, but will also include
random matrix aspects, while the second workshop will be geared
towards the analytic, stochastic and operator algebra aspects. In
the intervening two weeks we expect to organize a special program
aimed at bringing graduate students and postdoctoral fellows quickly
to frontiers of the subject by providing them with a short series
of lectures that covers the basic definitions and theorems.
Organizers for first workshop: R. Speicher, A. Belinschi, A. Guionnet,
and A.Nica
Organizers for second workshop: D.V. Voiculescu, H.Bercovici, B.
Collins, J. Mingo, and R.Speicher.
Back to top
