Multivariate Operator Theory (15w5020)


(University of Waterloo)

(Texas A & M University)

Joerg Eschmeier (Universitat des Saarlandes)

J. William Helton (University of California at San Diego)

(University of California at Santa Barbara)


The Banff International Research Station will host the "Multivariate Operator Theory" workshop from April 5th to April 10th, 2015.

Operator theory is a century-old field of mathematics with deep roots in mathematical physics and engineering
systems. During the last three decades the field has significantly broadened and changed due to the influx of
ideas and techniques pertaining to analytic function theory and differential geometry. This has led to new
questions and new results, which, in turn have allowed the investigation of completely new phenomena including
generalizations of probability theory and analysis to functions of both non commuting and free variables. The
resulting interdisciplinary topics of research, cover most of what is commonly known as multivariate operator
theory, and offer a wide spectrum of challenges for the working mathematician, new vistas for beginners, and
has endless applications to modern physics, statistics and engineering.

While everyone is accustomed to functions of numbers, increasingly technological problems involve large arrays
of data called matrices. Since matrix multiplication is not commutative, manipulation of matrices involves
important challenges that take one into the domain of free and non commutative multivariate operator theory.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).