Xi’an Jiaotong-Liverpool University Featured PhD Programmes
European Molecular Biology Laboratory (Heidelberg) Featured PhD Programmes

New computations in topological Hochschild and cyclic homology


Department of Mathematics

About the Project

Algebraic K-theory is an invariant of rings which connects algebraic topology to number theory. In 70s Quillen introduced higher algebraic K-theory groups and since then a lot of progress has been made in computing these groups. In general, it is very difficult to make such computations and a lot of tools have been developed to carry them out. Topological Hochschild and cyclic homologies are such tools (THH and TC).

This project will focus on concrete computations of THH and TC. More concretely, it will deal with THH and TC of certain differential graded algebras coming from number theory. Developments in the recent years have improved methods for computing these invariants and the project will extensively use the new technology.

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

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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