Modern society would be unrecognisable without digital communications technologies such as satellite communications, cell phones, portable music players, flash drives, GPS (global positioning system) navigation, and movies on demand. A key reason these technologies have become ubiquitous, widely accepted, and highly dependable is the critical support provided by embedded mathematical structures and algorithms that remain invisible to the user.

The requirement for embedded mathematics in these technologies derives from a combination of physical constraints, for example the desire to send information from one device to another using energy efficiently, or to pass information securely between two parties even though outsiders can monitor the exchange, or to recover transmitted information correctly despite corruption of the original signal by noise. These combinations of physical constraints correspond to mathematical problems of arranging objects subject to multiple constraints.

My research interests lie in combining combinatorial, algebraic, and analytical techniques to solve such classical and emerging problems of digital communications. I frequently use computers as an experimental tool to reveal patterns, identify key examples, improve intuition, and so point the way to new theoretical results.

Some areas of particular interest are:

- Constructions of Complex Equiangular Lines
- The Structure of Costas Arrays
- Wavelength Isolation Sequence Design
- The
*n*-Card Problem - Barker Sequences and Barker Arrays
- Golay Complementary Sequences and Arrays
- Power Control for Multicarrier Wireless Transmission
- The Peak Sidelobe Level of Binary Sequences
- The Merit Factor Problem
- The Structure of Difference Sets
- Coding for Transmission over Wires
- Modelling of Errors in Storage Devices