Noncommutative Functions Seminar

Date: September 14, 2018

Time: 10:00AM - 11:00AM

Location: BLOC 624

Speaker: Jurij Volcic, Texas A&M University

Title: An introduction to noncommutative function theory (2nd talk)

Abstract: The rise of noncommutative (nc) functions started in 1972 with the pioneering work of J. L. Taylor. Since then, there has been a vivacious development of this theory, fueled by free probability, operator spaces, control theory, complex analysis, and free real algebraic geometry. Each of these areas offer their own aspect of nc functions. In two lectures I will try to lay out a very basic framework following the exposition by Kaliuzhnyi-Verbovetskyi and Vinnikov. In the first (algebraic) lecture we will define nc sets,nc functions and nc difference-differential operators. The study of their properties will naturally lead to higher order nc functions and their difference-differential calculus, which will culminate with the Taylor-Taylor formula. The second (analytic) lecture will then introduce various topologies on nc sets, corresponding analyticities of nc functions, and of course a few fundamental theorems.