[School of Natural Sciences PhD Scholarships] Supergeometry, integration on supermanifolds, super exterior powers, and related structures.

About the project

About the Project Supermanifolds are analogs of differentiable (and complex-analytic) manifolds whose main new feature is the presence of "anticommuting" variables among local coordinates. (Physicists call them "fermionic variables" as opposed to "bosonic", which are ordinary commuting. They are related with the two fundamental classes of particles, known as bosons and fermions.) Their introduction was strongly motivated by physics, such as method of second quantization, quantization of non-abelian gauge fields and supersymmetry. Besides becoming standard language in physics, supermanifolds present an fascinating area of study themselves. There are many attractive directions, in particular those connected with integration theory, super differential forms and super exterior powers. Examples of recent work with open questions remaining include the quest for super cluster algebras and the Stanford-Witten formula for super-Liouville volume. 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 a discipline directly relevant to the PhD OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in a discipline directly relevant to the PhD. Previous research experience / a strong background in algebra and differential geometry is desirable. 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