Operator Theory Seminar
Abstract: The noncommutative functions discussed in this talk are limits of $n\times n$ - matrix-valued polynomials in $d$ $n\times n$ matrices. In particular, neither the values of the functions nor their inputs commute. These functions appear quite naturally in certain areas of mathematics and are the subject of the vibrant field of Geometric Invariant Theory. The point to be made in this talk and the talk of February 21 is that although these functions are presented as creatures of the planes of matrix variables, their natural habitat, the land in which they grow and thrive, is the forest of matrix bundles sprouting from the rich soil of matrix invariants.