School of Mathematics, Statistics and Physics

Staff Profile

Dr David Kimsey

Lecturer in Pure Mathematics

Background

Professional Appointments:

2016-present: Lecturer in Pure Mathematics, School of Mathematics and Statistics, Newcastle University, UK.


2013-2015: Postdoctoral fellow in the Department of Mathematics, Ben-Gurion University of the Negev, Israel. Supervisor: Daniel Alpay.


2011-2013: Postdoctoral fellow in the Faculty of Mathematics, Weizmann Institute of Science, Israel. Supervisor: Harry Dym.


Education:

2011: PhD in Mathematics from Drexel University, USA. Thesis title: Matrix-valued moment problems. Supervisor: Hugo J. Woerdeman.

2007: BSc in Mathematics from Drexel University, USA.


Languages:

English

Research

Broadly speaking, my research interests center around investigating connections between operator theory on quaternionic (complex) Hilbert spaces and quaternion-valued (complex-valued) function theory. In particular, multidimensional moment problems, orthogonal matrix polynomials and related asymptotics and spectral theory for operators on a quaternionic Hilbert space.

Spectral theory for normal operators on a quaternionic Hilbert space is motivated by connections to quantum mechanics and is quite delicate due to the noncommutativity of the quaternions. One quickly realises that the notion of spectrum is not immediately obvious. The proper notion turns out to be given by the recently discovered S-spectrum. In the recent paper, Alpay, Colombo and I produced a rigorous analogue of the spectral theorem for bounded and unbounded normal operators on a quaternionic Hilbert space. Related function theory and moment problems in quaternionic settings are also of interest and have been explored. 

Publications