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Mathematics PhD

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 as new posts have been filled. The main areas of interest in these groups are listed below. 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.

Our research interests include Rings and Algebras, Representation Theory, Geometric Group Theory, Algebraic Geometry and Topology, Noncommutative Probability and Operator Algebras, Banach Algebras and Spaces, Probability and Random Matrices, Partial Differential Equations in Mathematical Physics, Geometric Rigidity Theory, Rigidity and Flexibility of Frameworks and Discrete and Computational Geometry.

Students have a formal weekly meeting with their supervisor, but in most cases this is supplemented by more frequent, informal contact. Any skills gaps will be covered through additional lecture programmes or directed reading, and students have the opportunity to attend graduate lectures on topics of current research interest, attend courses given as part of the MAGIC consortium and take part in internal seminars for students and staff.

These are an ideal opportunity to gain valuable experience of communicating ideas to an audience while also receiving feedback, which can help set future research directions.

All PhD students have their own departmental laptop, and are generously supported to attend and present work at national and international conferences. Proposals are accepted in any areas of interest to the department.