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Computations and invariants in equivariant stable homotopy theory


Department of Mathematics

About the Project

Equivariant stable homotopy theory is one of the most active research areas in modern algebraic topology. It studies equivariant cohomology theories which are invariants of spaces with group actions. Such invariants are useful to study for example compact Lie group actions on smooth manifolds.

The most classical setup for equivariant stable homotopy theory considers compact Lie group actions. Recently a new setup of proper equivariant stable homotopy theory was developed. This studies infinite discrete group actions by means of proper equivariant cohomology theories. The goal of this project is to make new computations of these cohomology theories and relate the calculations to geometric group theory. The subject is fairly new. However, a lot of tools have been developed recently to make new calculations in this direction.

Applicants should have (or expect to achieve) a UK first class honours degree in Mathematics, or a 2:1 honours degree in Mathematics alongside a Masters with Merit or Distinction, also in Mathematics with knowledge of - Algebraic topology, stable and unstable homotopy theory, basic homological algebra and category theory.

No prior knowledge of equivariant stable homotopy theory is needed.


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

Informal inquiries can be made to Dr Irakli Patchkoria () 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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