Global St Andrews and Bonn Doctoral Scholarship - Mathematics and Statistics

Project

One way that mathematicians simplify the structure of a mathematical object is to describe a set of “generators” for the object and the relations between those generators. For example, you can describe every address in a city by giving directions from a starting point (i.e., “go straight three times, then turn right, then go…”). Thus, you can simplify the set of all addresses to a few simple operations (turn left, turn right, go straight). The price that you pay is that the descriptions might not be unique (i.e., straight, left, straight will frequently bring you to the same place as left, straight, right, straight), so you need to understand the relationships between the generators right, left, and straight. It’s also desirable to know the “optimal” way to describe an address in terms of these directions. In the past five years, techniques from geometry have provided new methods for understanding how to generate objects from algebra; furthermore, they relate the concept of dimension in geometry to optimal generation time.

More precisely: objects in algebra are generated by algebraic equations. For instance, if you wanted to describe a circle in three-dimensional space, you might write down the equations x² + y² = 1, z = 0. This is the most efficient way to describe the circle as a subset of three- dimensional space, and reflects that the circle is 1-dimensional, while the ambient space is 3- dimensional (and we have 3-1=2 equations). One interpretation of an open problem in algebra (Orlov’s Conjecture) asks: can you build all of the geometric subsets of an n-dimensional space using at most n equations?

For this, the project will turn to a different area of mathematics: symplectic geometry. This relatively new research area studies geometry related to physical systems like planetary orbits and the dynamics of pendulums. A surprising connection (the “mirror symmetry conjecture”) posits that problems from algebra can be translated into symplectic geometry instead. In the last few years, the proposed supervisors (Prof. Laurent Cote, Dr. Jeff Hicks) have used this method to prove Orlov’s conjecture in a variety of settings. This work represents a major advancement in the area. The proposed research will settle Orlov’s conjecture for a large class of algebraic spaces of interest to the mathematical community (“large complex structure limits”). In addition to being an interesting example of spaces in its own right, it provides a key step in proving Orlov’s conjecture for all Batyrev mirror spaces. The project has the advantage that while several of the fundamental cases have already been worked out in detail, the general case will require the development of new techniques and place the doctoral student on an excellent trajectory for developing their own research programme in categorical symplectic/algebraic geometry.

The project will be managed jointly between the School of Mathematics and Statistics at St Andrews and the Mathematical Institute at Bonn. The student will be supervised by Dr Jeff Hicks (St Andrews) and Prof. Laurent Côté (Bonn).

Informal enquiries regarding this scholarship are encouraged  and may be addressed to the co-supervisors:

Dr Jeff Hicks (jeff.hicks@st-andrews.ac.uk)

Prof. Laurent Côté (lcote@math.uni-bonn.de)

Value of award (per year)

The funding comprises a scholarship equivalent of a full-fees award and stipend for a period of up to 3.5 years. It is expected that the student will spend half of the scholarship term at the University of St Andrews and half at the University of Bonn:

• For the period spent at the University of St Andrews, the scholarships will comprise a full tuition fee award and an annual stipend paid at a rate set by the University of St Andrews. For 2025-2026, the stipend is £19,775 p.a., with an annual uplift published by the University each academic year.

• For the period spent at the University of Bonn, the scholarship will comprise a monthly maintenance grant of €1,800. The University of Bonn does not charge any tuition fees, but students must pay a so-called social contribution once per semester (currently €315 per semester).

Unless otherwise specified, the scholarships do not cover:

• Any continuation, extension, or resubmission period/fees.
• A research training grant or another equivalent award for research expenses.
• Support for travel, immigration, health insurance and related charges between the partner institutions.

Duration of award

Up to 3.5 years. The student will be expected to spend approximately half of the award term at the University of St Andrews and half at the University of Bonn. The successful candidate will be expected to have completed the doctorate degree by the end of the award term. The award term excludes the continuation period and any extension periods.

Additional criteria

Applicants must not already (i) hold a doctoral degree; or (ii) be matriculated for a doctoral degree at either the University of St Andrews or the University of Bonn (or another institution).

How to apply

Submit an application to Dr. Jeff Hicks (jeff.hicks@st-andrews.ac.uk) with subject line “Global Doctoral Scholarship: [Name of Applicant]”.  Expressions of interest should include the following documents:

• Cover letter,
• CV,
• Transcripts of most relevant/recent degrees,
• Statement of research interests of the candidate, and
• Two academic references (name email address)

Following a successful application for the scholarship, candidates may be invited to submit an application to both universities for admission into the program and award of the scholarship.

Please indicate in your application that you wish to be considered for this Global doctoral scholarship (Côté and Hicks). Applications should be submitted to the co-supervisors via email to: Dr Jeff Hicks (jeff.hicks@st-andrews.ac.uk).

Next steps

Successful scholarship applicants will be invited to apply for admission to both universities from April 2026, and then formal outcomes of the position will be made, subject to provision of full application details and materials for entry to the programme at the agreed entry point in 2026-2027.

Successful scholarship applicants must meet all relevant entry requirements for admission including any immigration requirements that may be in place. Please see the advice on applying for research degree programmes at St Andrews and the PhD application guidelines at Bonn.

Terms and conditions

Terms and conditions of scholarships for St Andrews can be found here: Awards general terms and conditions.

These are applicable during the St Andrews duration of the award. Please consult the partner institution for their terms and conditions relating to scholarships.

Awards are subject to final signatures of contractual relationships between the parties, and are not an indication of admission to the doctoral programme. Successful scholarship applicants must apply to both institutions and meet all relevant entry requirements for admission including any immigration requirements that may be in place.

When will I know the outcome?

By mid-April 2026. Awards are subject to final signatures of contracts between the parties and successful admission to both institutions.