Theory of Functions of Noncommuting Variables and Its Applications (10rit141)


(Drexel University)

Victor Vinnikov (Ben Gurion University of the Negev)


The Banff International Research Station will host the "Theory of Functions of Noncommuting Variables and Its Applications" workshop from February 21st to February 28th, 2010.

The proposed research deals with functions on matrices of all sizes satisfying certain compatibility conditions as we vary the
size of matrices (respecting direct sums and simultaneous similarities). These functions come equipped with a noncommutative difference-differential calculus. Our approach integrates
various approaches of other researchers in this area, leading us to a unified theory. We expect important applications to noncommutative polynomials and rational functions, especially in
the problems arising from the study of linear matrix inequalities (LMIs) in control. We also expect applications to free probability
and to spectral theory (functional calculus) for noncommuting operators.

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 Tecnolog�a (CONACYT).