Free Probability, Extensions, and Applications (08w5076)


(University of Waterloo)

(Queen's University)

Antonia Tulino (Università degli Studi di Napoli Federico II)

Dan-Virgil Voiculescu (UC Berkeley)


Free Probability is a recent mathematical theory which tries to understand
non-commutative algebras (as they appear, e.g., in quantum mechanics) by
using techniques inspired by classical probability theory. This approach
has been very succesful, solving some longstanding problems in the field of
operator algebras. Quite surprisingly, it has turned out that the methods
and results of free probability can also be used to describe the spectral
properties of random matrices. The latter appear in many models in applied
sciences; e.g., Wishart random matrices are at the basis of modern statistics
and similar kind of random matrices are used to model wireless communication
by electrical engineers. The proposed workshop will aim at developing free
probability further, with particular emphasis towards its applications.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).