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Algebraic groups, geometric invariant theory 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. 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.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in Mathematics and knowledge in Algebra, group theory. Some knowledge of algebraic geometry would be useful but is not essential.

APPLICATION PROCEDURE:

• 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
• Details of 2 academic referees

Informal inquiries can be made to Prof Ben Martin () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of Mathematics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS.

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