Operator Theory Seminar
Abstract: The functions that I will describe can be usefully represented as sections of a certain matrix bundle. The base of that bundle is an abstractly defined complex algebraic variety with singularities. The Kempf-Ness theorem enables one to realize this variety more concretely, from topological and analytic perspectives, as the quotient space of a space of matrices on which the projective unitary group acts. This concrete realization, in turn, provides a way of parametrizing certain important invariants of the algebras that the functions generate.