Rational points and arithmetic statistics

Postgraduate Studentships; Bath; Hybrid; GBP 21,000 - 23,000; Full time

Job summary

The University of Bath invites applications for a PhD position in Rational points and arithmetic statistics. This is part of the EPSRC programme grant Unifying Arithmetic Statistics and runs for 5 years starting Oct 2026. The successful candidate will be based at Bath and work with lead supervisor Prof. Daniel Loughran.

The project combines algebraic geometry and number theory, with strong emphasis on collaboration across partner universities. Funding includes a stipend and tuition coverage.

Qualifications

• Applicants should hold, or expect to receive, a First Class or good Upper Second Class UK Honours degree (or the equivalent) in a relevant subject.
• A master’s level qualification would also be advantageous.

Responsibilities

• Fully integrated within the programme grant activities, including collaborative retreats, summer schools, study groups, conferences, and opportunities for secondments at partner universities.
• Work on topics related to rational points and arithmetic statistics as part of the PhD project.

Education

First Class or good Upper Second Class UK Honours degree (or the equivalent) in a relevant subject

Master’s level qualification would be advantageous

Job description

Rational points and arithmetic statistics

ThisisaPhDpositiontojointheEPSRCprogrammegrant,UnifyingArithmeticStatistics. This programme grant runs for 5 years starting in October 2026 and is joint between Bath, Kings College London, Cambridge, and Glasgow. You will be based at Bath and supervised by the project lead, Professor Daniel Loughran.

The PhD project will require a mix of tools from algebraic geometry, algebraic number theory, Galois theory, and analytic number theory. It will work on some of the programme grant objectives, which concern applications of the theory of rational points on varieties to problems in arithmetic statistics, including some of the following topics:

• Distributionsofnumberfieldsandclassgroups
• Local-globalprinciples,includingtheBrauer-ManinobstructiontotheHasseprincipleandweakapproximation
• Existenceanddistributionofrationalpointsonvarietiesandstacks
• TheinverseGaloisproblem

As part of the PhD project you will be fully integrated within the programme grant activities, which will include collaborative retreats, summer schools, study groups, conferences, and opportunities for secondments at the partner universities.

Funding is currently available for at least 3 years.

References

[1] Daniel Loughran, Tim Santens, The leading constant in Malle's conjecture, https://arxiv.org/abs/2606.04983
[2] Daniel Loughran, Tim Santens, Malle's conjecture and Brauer groups of stacks, https://arxiv.org/abs/2412.04196
[3] Daniel Loughran, Ross Paterson, Lower bounds for A4-quartic fields, https://arxiv.org/abs/2510.05248

Entry Requirements

Applicants should hold, or expect to receive, a First Class or good Upper Second Class UK Honours degree (or the equivalent) in a relevant subject. A master’s level qualification would also be advantageous.

Candidates may be considered for a University of Bath studentship tenable for a minimum of 3 years. Funding covers tuition fees, a stipend (£21,805 p/a in 2026/7) and access to a training support budget.

• IntheFundingyourstudiessection,select‘University-LURS’asthestudentshipforwhichyouareapplying.
• IntheYourPhDprojectsection,quotetheprojecttitleofthisprojectandthenameoftheleadsupervisorintheappropriateboxes.

Failuretocompletethesetwostepswillcausedelaysinprocessingyourapplicationandmaycauseyoutomissthedeadline.

MoreinformationaboutapplyingforaPhDatBathmaybefoundonour website .

PLEASE BE AWARE: Applications for this project may close earlier than the advertised deadline if a suitable candidate is found. We therefore recommend that you contact the lead supervisor prior to applying and submit your formal application as early as possible.

Equality,DiversityandInclusion:

We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.

If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.

Who is eligible to apply?

The Faculty of Science at the University of Bath has studentships available for Home and Overseas students. However, in line with UKRI policy, the number of studentships available to Overseas students are capped.

A world-class University in a World Heritage city At Bath, we are known for excellence in teaching and research, o...