Job Description
Project details
Recently Morier-Genoud and Ovsienko introduced the notion of q-numbers as certain quantisation of real numbers. Remarkably these numbers turned out to be related to many areas of mathematics: cluster algebras, Schubert calculus, Bridgeland stability and knot theory.
The main aim of this three-year PhD project is to extend this fastly growing theory in various directions, including geometry, group theory and dynamics. This will include the study of the Markov polynomials, which can be viewed as 3-parameter quantisation of the celebrated Markov numbers.
Other topics may include Markov-like dynamics over Clifford’s dual numbers and the special actions of some classical arithmetic groups.
94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Supervisors
Primary supervisor:Â Alexander P. Veselov
Secondary supervisor:Â Brian Winn
Entry requirements
Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours.
Entry requirements for United Kingdom
The successful candidate should have the First Class (or equivalent) degree in Mathematics and be familiar with the basics of number theory, topology and group theory.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Fees and funding
Tuition fees for 2025-26 entry
UK fee
£5,006 Full-time degree per annum
International fee
£22,360 Full-time degree per annum
Fees for the 2025-26 academic year apply to projects starting in October 2025, January 2026, April 2026 and July 2026.
Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.
How to apply
All applications should be made online. Under programme name, select Mathematical Sciences. Please quote the advertised reference number:MA/AV-SF1/2025 in your application.
To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents.
The following selection criteria will be used by academic schools to help them make a decision on your application. Please note that this criteria is used for both funded and self-funded projects.
Please note, applications for this project are considered on an ongoing basis once submitted and the project may be withdrawn prior to the application deadline, if a suitable candidate is chosen for the project.
