SCIENTIFIC PROGRAMS AND ACTIVITIES
|May 24, 2013|
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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.
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, July 2 - 6, 2013, will be more on the combinatorics
side, but will also include random matrix aspects, while the second
workshop, July 22 - 26, 2013, 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.