# Pure Mathematics

The principal research activity in pure mathematics at Lancaster over the last 20 years has concerned mathematical analysis and a strong international reputation has been established in this field. During the last five years, an algebra group of similar strength has been created and recent new posts have established a probability group too. In addition, a group at the interface between algebra, analysis and combinatorics study geometric rigidity theory.

We also have links with researchers across the UK and internationally, through research networks such as QOP, NBFAS and ARTIN, as well as more informal connections and collaborations.

## Algebra and Geometry

The Algebra and Geometry group conducts research in a wide variety of subjects of algebraic and geometric nature, including group theory, representation theory and homological algebra.

Algebra and Geometry## Analysis and Probability

Research areas of the Analysis and Probability group include noncommutative probability, random matrices, operator and Banach algebras, operator theory, PDEs, scaling limits in stochastic models, applied probability and stochastic approximation.

Analysis and Probability## Discrete Mathematics and Geometric Rigidity

Geometric Rigidity theory is concerned with the rigidity of structures which are defined by geometric constraints (fixed lengths, fixed areas, fixed directions, etc.) on a set of rigid objects (points, line segments, polygons, etc.).

Discrete Mathematics and Geometric Rigidity