Organizers

Dr Zinaida Lykova, Dr Michael Dritschel, Dr Evgenios Kakariadis, Dr David Kimsey.


Objective

Our topic will be a powerful machinery that has been developed in the last 60 years both to discover and to prove theorems about analytic functions in one and several complex variables through the construction of operators on Hilbert space.

The lectures will begin with expositions of the elementary operator theory that is required to achieve interesting results in function theory.

Next we will show how a number of classical results in the theory of analytic functions in one variable, when cast in a Hilbert space setting, can be proved by operator-theoretic methods which are largely algebraic in nature. These results will include the Herglotz Representation Theorem, the Caratheodory and Pick Interpolation Theorems, Nevanlinna's Representation Theorems, the Caratheodory-Julia Theorems, and Loewner's Theorem.

The remainder of the talks will focus on how the operator-theoretic proofs of these one- variable theorems can be generalized to yield a variety of new results in several complex variables.


LMS Invited Lecture Series 2017: Professor Jim Agler

Jim Agler is a Professor of Mathematics at the University of California, San Diego. He has made deep contributions to mathematical analysis; he is also an outstanding expositor. His work has had a profound inuence on operator theory, interpolation theory, several complex variables and noncommutative analysis. Personal webpage: here.


Other Speakers

Professor John McCarthy

John McCarthy is a Professor at Washington University in St. Louis, USA. His research interests are Analysis, especially Operator Theory and one/several Complex Variables. Personal webpage: here.

Associate Professor Greg Knese

Greg Knese is an Associate Professor at Washington University in St. Louis, USA. His research interests are Complex Function Theory, Operators, Harmonic Analysis. Personal webpage: here.

Assistant Professor Kelly Bickel

Kelly Bickel is an Assistant Professor at Bucknell University, Lewisburg, PA, USA. Her research interests are Multivariate Operator Theory, Several Complex Variables, Harmonic Analysis. Personal webpage: here.


Poster

The poster for the meeting is available here.


Acknowledgements

We acknowledge support from the London Mathematical Society and the School of Mathematics and Statistics, Newcastle University.

The annual Invited Lecturers scheme aims to bring a distinguished overseas mathematician to the United Kingdom to present a small course of about ten lectures spread over a week. Each course of Invited Lectures is on a major field of current mathematical research, and is instructional in nature, being directed both at graduate students beginning research and at established mathematicians who wish to learn about a field outside their own research specialism.