Operator Theory Seminar
In these talks, which are based on long collaborations with Baruch Solel, I will discuss how to view certain tensor algebras as algebras of noncommutative analytic functions. In a sense that I will make precise, tensor algebras are noncommutative analogues of polynomial algebras, and the function theory I will describe is a noncommutative analogue of the theory of polynomial and analytic functions that one studies in basic analysis courses, such as MATH 5210. The fundamental principle underlying what I will discuss is the observation that every ring may profitably be analyzed as a ring of functions defined on its space of representations (i.e. its modules). In contemporary algebro-geometric language, every ring may be realized as an affine scheme.