Past Student Colloquia

At a young age we are exposed to the Spectral Theorem for normal and/or self-adjoint linear operators on finite dimensional complex vector spaces; ofttimes at an age too young to appreciate its importance.

In this talk we will discuss the Spectral Theorem for normal operators on (not necessarily finite dimensional) Hilbert space. As an application of the Spectral Theorem we will talk about the $L^\infty$ functional calculus for normal operators. This will land us in the world of abelian von Neumann algebras. Happily, the functional calculus alone will allow us to describe all abelian von Neumann algebras.

Time permitted, we will finish early.