Advanced Mathematics

Applying advanced mathematical theory and methods for cybersecurity, data protection and privacy, and trustworthy digital systems.

About us

The Department of Mathematics includes several internationally recognised scholars working on projects relevant to digital trust and cybersecurity, both independently and alongside researchers from other clusters in interdisciplinary projects.

Mathematics is central to many aspects of digital trust, for example:

  • probability theory underpins differential privacy;
  • abstract algebra formalises homomorphic encryption;
  • data and model parallelism is at the epicentre of federated learning;
  • statistics provides methods for data augmentation.

Research

Examples of research in the Mathematics Department related to the advanced mathematics cluster, include:

  • privacy-preserving data analysis;
  • defence against data-poisoning attacks on neural networks;
  • adversarial robustness of Laplacian learning;
  • data augmentation via optimal transport;
  • data augmentation based on topological data analysis;
  • group theory with applications to digital cryptography.

People

Cluster Lead: Theodore Papamarkou.

Members: Prof Mark Kambites, Dr Matthew Thorpe, Prof Peter Rowley.