Colloquium Speaker:
Dr. Robert Martin, Ph.D.
University of Manitoba, Winnipeg, Manitoba
Title: Entire and meromorphic functions of several non-commuting variables
Abstract: We study the ring of entire functions, Od, in d ∈ N non-commuting (NC) variables. Elements of Od are bona fide holomorphic and analytic functions on the d−dimensional “NC universe” of all d−tuples of complex, square matrices of all fixed, finite sizes. Here, by “holomorphic” we mean “differentiable” and by “analytic” we mean “admit certain Taylor-type power series expansions with non-zero radii of convergence”. We construct two natural candidates for the “field of fractions” of Od. These are noncommutative fields whose elements we would like to interpret as NC meromorphic functions. The relationship between these two fields and several open problems will be discussed.
Day & Time: Thursday, March 5, 2026, at 3:00pm
Location: Lambton Tower, Room 9-118
Counts toward seminar attendance for MSc and PhD students in Math & Stats.