NC function theory: The non-Commutative Frontier of Analysis and Algebra (25w5371)


Robert T.W. Martin (University of Manitoba)

(University of Waterloo)

Quanlei Fang (CUNY)

Eli Shamovich (Ben-Gurion University of the Negev)

Jurij Volcic (Drexel University)


The Banff International Research Station will host the “NC function theory: The non-Commutative Frontier of Analysis and Algebra” workshop in Banff from May 4 - 9, 2025.

Non-commutative Function Theory is a powerful extension of classical complex analysis to several non-commuting (NC) variables with fundamental connections and applications to NC Algebra, Free Analysis and Operator Algebra Theory. Non-commutative functions are functions of $d-$tuples of square matrices of any fixed size, whose outputs are matrices of the same size, and which have certain natural invariance properties enjoyed by polynomials in several non-commuting variables. Many classical and several complex variables results extend naturally to this NC setting with a blend of algebraic and analytic proofs. Recent and exciting progress in NC Function Theory has been catalyzed by the injection of both analytic and algebraic methods. This workshop will bring together recognized research leaders in these fields to share their expertise, foster interdisciplinary collaborations, and further accelerate the development of NC Function Theory and 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 U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.