Overview

The beautiful and far-reaching theory of functions of a complex variable is one of the great achievements of mathematicians of the late 19th and early 20th centuries.

The theory, to this day, remains very active and plays an essential role in many branches of mathematics, physics and engineering. One notable application is to spectral theory, which is a powerful tool in the study of operators on Hilbert space, both bounded and differential.

We are interested both in the application of complex analysis to operators and in the use of operator theory to prove results in complex analysis.

Another application is to control theory, where, for example, the problem of designing an automatic controller for a class of engineering devices can be reduced to the construction of analytic matrix-valued functions on a half-plane meeting some specifications. The latter application makes contact with the theory of functions of several complex variables, which has been extensively developed since the 1920s.

Staff

The following members of staff from the School of Mathematics and Statistics are members of the Complex Analysis research group.