Free Noncommutative Function Theory

Speaker
Prof. Victor Vinnikov (Ben-Gurion University)
Date
21/01/2018 - 13:00 - 12:00Add to Calendar 2018-01-21 12:00:00 2018-01-21 13:00:00 Free Noncommutative Function Theory Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity properties of usual analytic functions) and admit a good difference-differential calculus. Noncommutative functions appear naturally in a large variety of settings: noncommutative algebra, systems and control, spectral theory, and free probability. Their study originated in the groundbreaking work of J.L. Taylor on noncommutative spectral theory in the 1970s, but it is mostly in the last decade that the theory established itself as a new and active research area. I will survey some aspects of these developments, including (if time permits) recent work on interpolation and extension problems. The talk will be aimed at a general mathematical audience and should be accessible for graduate students (or even advanced undergraduates). Colloquium room, Mathematics Dept.,building 216 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Colloquium room, Mathematics Dept.,building 216
Abstract

Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity properties of usual analytic functions) and admit a good difference-differential calculus. Noncommutative functions appear naturally in a large variety of settings: noncommutative algebra, systems and control, spectral theory, and free probability. Their study originated in
the groundbreaking work of J.L. Taylor on noncommutative spectral theory in the 1970s, but it is mostly in the last decade that the theory established itself as a new and active research area. I will survey some aspects of these developments, including (if time permits) recent work on interpolation and extension problems. The talk will be aimed at a general mathematical audience and should be accessible for graduate students (or even advanced undergraduates).

Last Updated Date : 15/01/2018