Fully Funded EPSRC PhD Scholarship: Motivic Category Theory and Rational Motivic Gamma-spaces

Closing date: Position is open until filled. Applications will be assessed on a rolling basis.

Start date: October 2020 or January 2021

Project Supervisor: Dr Grigory Garkusha

The primary goal of motivic homotopy theory is to study algebraic varieties from a homotopy theoretic viewpoint. Many of the basic ideas and techniques in this subject originate in algebraic topology. The theory was invented by Morel and Voevodsky in the 90s and it is now one of the most active areas in algebraic geometry and algebraic topology, bringing together researchers in topology, algebra and representation theory. Motivic homotopy theory led to such striking applications as the solution of the Milnor conjecture and the Bloch- Kato conjecture, in algebraic geometry. Besides these quite spectacular applications, the fact that one can use the ideas and techniques of homotopy theory to solve problems in algebraic geometry has attracted mathematicians from both fields and has led to a wealth of new constructions and applications.

This project will investigate categorical aspects of various triangulated categories of motives and rational motivic Gamma-spaces. The main purpose of this project is to advance our understanding of enriched motivic category theory, rational connected motivic spectra and motivic infinite loop spaces. Important applications for a range of associated cohomology theories of algebraic varieties and for the classical stable homotopy theory are expected as well.

Candidates must have a first, upper second-class honours or a Master’s degree with Merit, in a relevant discipline.

For candidates whose first language is not English, we require IELTS 6.0 (with 5.5 in each component) or equivalent. Please visit our website for a list of acceptable English language tests. We prefer candidates to have already met the English Language requirements at the point of application, although this is not a requirement.

Studentships funded by EPSRC are subject to UK/EU residency eligibility. Normally, this means to be eligible for a full award (fees plus stipend) you must:

- Have been ordinarily resident in the UK, meaning there are no restrictions on how long you can stay, and;
- Have been ’ordinarily resident’ in the UK for at least three years prior to the start of the Studentship grant, and;
- Have not been residing in the UK wholly or mainly for the purpose of full-time education. (This does not apply to UK nationals and EU nationals who were ordinarily resident in the EU immediately before the period of full-time education).

For this particular EPSRC opportunity, we are also able to consider your application if you are an EU national who does not meet the residential eligibility criteria outlined above; this is possible through EPSRC’s flexibility regarding `open eligibility’.