Categorification in Representation Theory (MIEMIETZV_U26EMP)
Key Details
- Application deadline
- 31 January 2026 for International, 31 March 2026 for Home
- Location
- UEA
- Funding type
- Self-funded
- Start date
- 1 June 2026
- Mode of study
- Full-time
- Programme type
- PhD
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Project description
Primary supervisor - Prof Vanessa Miemietz(opens in a new window)
Categorification has led to major advances in representation theory in the last 25 years, such as the proof of Broué’s abelian defect group conjecture for symmetric groups and the proof of the Kazhdan—Lusztig conjectures for all Coxeter types.
Classically, a representation of an algebra is an action of the latter on a vector space via linear maps. This is categorified to an action of a monoidal category on another category, or more generally of a 2-category on a collection of categories, via (nice) functors. By studying categorifications, one can obtain new information about both the original algebra and the categories one is acting on. There are many open questions about the general theory of such higher representations, as well as about specific examples.
This project will focus on understanding specific examples. Prerequisites are a good understanding of algebras and their representations. Additional knowledge of some category theory would useful.
Entry requirements
The standard minimum entry requirement is 2:1 in Mathematics.
Funding
This project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found here(opens in a new window).
A bench fee is also payable in addition to the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.
UEA Alumni 10% Scholarships(opens in a new window) - A scholarship of a 10% fee reduction is available to UEA Alumni looking to return for postgraduate study at UEA, Terms and conditions(opens in a new window) apply. For a postgraduate master’s loan, visit our Postgraduate Student Loans(opens in a new window) page for more information.