CMSA Q&A Seminar

Speaker: James Eldred Pascoe, Drexel University

Title: (What is) The tracial fundamental group and free universal monodromy?

Abstract: We introduce the tracial fundamental group to classify the analytic continuation of functions that are locally behave like the trace of natural matrix valued functions. While globally defined natural matrix-valued functions (known as free noncommutative functions, which roughly locally are defined by noncommutative power series) satisfy universal monodromy, we show that these tracial free functions exhibit a rigid but nontrivial structure governed by the aforementioned group. We prove that the tracial fundamental group is always a torsion-free, divisible abelian group, standing in sharp contrast to the non-abelian fundamental groups of classical domains.