We use computers to manipulate representations of algebraic and geometric concepts, with applications to topics such as cryptography, security and engineering. We are the UK's leading centre for this work in computational mathematics and its applications. We are the EU centre of expertise on interfacing computer algebra to numeric calculations.

We use mathematical structures to put computer science on firm theoretical foundations. We are concerned with the mathematical understanding of logical reasoning, of programs, of processes, of programming languages, and of theorem provers.

Our methods include ideas and techniques from category theory, game theory, model theory, proof theory and type theory, as well from more traditionally computational topics such as automata, formal languages and computability.