Title: Lecture 1: Some consequences of von Neumann dimension
Speaker: Vaughan Jones (Vanderbilt University)
Abstract: In the 1930’s Murray and von Neumann gave a notion of continuous dimensionality for certain vector spaces (whose ordinary dimension is of course infinite) using what are now called von Neumann algebras. After defining this notion of dimension we will describe some results, in areas that are a priori quite different from von Neumann algebras, which are simple consequences of von Neumann dimension but have no known proof otherwise. Our main interest will be in the area of analytic number theory, in particular the study of cusp forms (which we will of course define!).