Combinatorial Representation Theory: Partitions and Basic Sets

About the Project

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.

The representation theory of many families of finite groups can be presented in terms of combinatorial objects. The most famous example is the symmetric groups, where the irreducible complex representations are parametrized by partitions. Other groups, such as the double covers of symmetric and alternating groups, or the infinite family of complex reflection groups, require the use of bar-partitions, or of tuples of partitions with certain properties.

The aim of this project is to develop a fuller understanding of these combinatorial objects, and to use it to better describe the representation theory of groups such as complex reflection groups, or the general linear group.

Of particular interest is the concept of basic set, which can provide some insight in the modular representation theory of finite groups (i.e. over fields of prime characteristic), while in fact working solely over fields of characteristic zero. One major component of this project will be the description of basic sets for various infinite families of finite groups, and their use for producing new information about the decomposition matrices and Brauer characters of these groups.

The project could be run distance mode.

Informal enquiries can be made by contacting Dr J B Gramain (jbgramain@abdn.ac.uk).

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in Pure Mathematics. Potential candidates The student must have Knowledge of Group Theory and Representation Theory of Finite Groups.

We encourage applications from all backgrounds and communities, and are committed to having a diverse, inclusive team.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Degree of Doctor of Philosophy in Mathematics to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project titleon the application form. If you do not include these details, it may not be considered for the project.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts .

Please note: you do not need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at researchadmissions@abdn.ac.uk

Funding Notes

This is a self-funding project open to students worldwide. Our typical start dates for this programme are February or October.

Fees for this programme can be found here Finance and Funding | Study Here | The University of Aberdeen.