[School of Natural Sciences PhD Scholarships] Homotopy Type Theory and Higher Categories

About the project

About the Project The project seeks to push forward the exploration of exciting new connections between two previously unrelated areas of Pure Mathematics: Mathematical Logic and Algebraic Topology. Since their discovery around 2008, these connections have led to the creation of the area of Homotopy Type Theory and to the Univalent Foundations programme of Fields Medallist Vladimir Voevodsky, with impact on the development of new computer systems for the verification of mathematical proofs. The project will focus on the counterpart in this setting of the fundamental correspondence between type-theoretic axioms and category-theoretic structure, building on the development of higher category theory. In particular, topics to be investigated include: (1) cartesian closed and differential structure, building work of the main supervisor and collaborators in "Monoidal bicategories, differential linear logic, and analytic functors", Journal of the European Mathematical Society, 2026. (2) exact completions, building on work of the main supervisor and collaborators in "The effective model structure and ∞-groupoid objects", Forum of Mathematics, Sigma, 2022. 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, Mathematical Logic or other related subject OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Pure Mathematics, Mathematical Logic or other related subject. A good knowledge of category theory is desirable. This project will remain open until filled. If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026. If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

Research areas