PhD Thesis Defense

Tuesday, June 7, 2016 10:00 am - 10:00 am EDT (GMT -04:00)

Michael Hartz, Department of Pure Mathematics, University of Waterloo

"Nevanlinna-Pick spaces and dilations"

I will present some of the results in my thesis. A large part of the
talk will be devoted to Nevanlinna-Pick spaces and their multiplier
algebras. These algebras occupy an important place at the interface
between operator algebras, operator theory and complex analysis. I will
talk about the classification problem for these algebras from three
different points of view: Multiplier algebras associated to embedded
discs in the Drury-Arveson space, multiplier algebras of homogeneous
varieties, and the Borel complexity of the classification problem.

Moreover, I will indicate that the Hardy space on the unit disc is
essentially the only Nevanlinna-Pick space whose multiplication
operators are all hyponormal.

Finally, I will talk about dilations and von Neumann's inequality. While
it is known that there are three commuting contractions which do not
satisfy von Neumann's inequality, I will present a result which shows
that von Neumann's inequality holds for all multivariable weighted
shifts. This provides a positive answer to a question of Lubin and Shields.