Project description

Primary supervisor - Prof Vanessa Miemietz

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.

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 - A scholarship of a 10% fee reduction is available to UEA Alumni looking to return for postgraduate study at UEA, Terms and conditions apply. For a postgraduate master’s loan, visit our Postgraduate Student Loans page for more information.

Categorification in Representation Theory (MIEMIETZV_U26EMP)

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Project description

Entry requirements

Funding