Groups, Subgroups and Boundedness

Project Description

Group theory is the mathematical study of symmetry. Algebraic groups are certain groups of matrices with entries coming from a field such as the real numbers, the complex numbers or the integers modulo a prime. They are important in many areas of pure mathematics including number theory, representation theory and the theory of buildings. Their study combines ideas from algebraic geometry (the geometry of polynomials) and group theory.

In recent years some powerful geometric techniques were introduced to prove results about algebraic groups and related mathematical objects such as lattices. The aim of this project is to investigate new applications of these techniques to the structure of algebraic groups and the spaces that they act on. Some possible directions for research include geometric invariant theory, spherical buildings, the subgroup structure of algebraic groups over non-algebraically closed fields and boundedness for normal generating sets.

Funding Information

This PhD project has no funding attached and is therefore available to students (UK/International) who are able to seek their own funding or sponsorship. Supervisors will not be able to respond to requests to source funding. Details of the cost of study can be found by visiting View Website.

Eligibility Requirements

Selection will be made on the basis of academic merit. The successful candidate should have, or expect to obtain, a strong 1st Class degree in pure mathematics from a UK university, or international equivalent. Knowledge of algebra and group theory. Some knowledge of algebraic geometry would be useful but is not essential.

Application Process

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

  • Apply for Degree of Doctor of Philosophy in Mathematics
  • State name of the lead supervisor as the Name of Proposed Supervisor
  • State ‘Self-funded’ as Intended Source of Funding
  • State the exact project title on the application form

When applying please ensure all required documents are attached:

  • All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
  • Detailed CV, Personal Statement/Motivation Letter and Intended source of funding

Informal inquiries can be made to Prof Martin ([email protected]) with a copy of your curriculum vitae and a brief description of why you are interested in this project, along with full undergraduate transcript (and Masters transcript, if applicable). All general enquiries should be directed to the Postgraduate Research School ([email protected]).

To apply for this PhD, please use the following application link: https://www.abdn.ac.uk/pgap/login.php

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