[School of Natural Sciences PhD Scholarships] Lie algebra actions on noncommutative rings

About the project

About the Project The project will investigate Clifford and Weyl algebras, and related algebraic structures, arising from quadratic modules for semisimple Lie algebras and quantum groups. An example of a quadratic module is the adjoint representation; the structure of its Clifford algebra was described by Kostant in 1997. Much more recent results were obtained by Joseph, Alekseev-Moreau, Ion, Panyushev, De Concini-Papi-Procesi, Bazlov, and Ademehin. The project will bring together modern techniques from representation theory, quantum algebra and noncommutative geometry, and its importance will be both in applying quantum methods to representations and in obtaining new quantum group objects and categories, potentially leading to constructions of interest to theoretical physics. The student will receive training in the form of PhD-level taught courses, including the courses delivered by the MAGIC PhD taught course centre. The project will start with a guided literature review. The project may make substantial use of symbolic algebraic computation, and the student will be supported in developing proficiency in computer algebra systems such as SageMath for the exploration of the mathematical structures arising in the research. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Pure Mathematics OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Pure Mathematics. This project will remain open until filled. If your application is submitted by 1 st November 2026, you can expect a decision by 18 th December 2026. If your application is submitted by 15 th January 2027, you can expect a decision by 30 th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

Research areas