Modularity of vertex operator algebras for 3d superconformal field theories and symplectic singularities

About the Project

The Faculty of Science and Engineering at Maynooth University are pleased to announce that a Maynooth University Doctoral Scholarship in the Department of Mathematics and Statistics will be available for a suitably qualified and successful applicant intending to commence their PhD studies in October 2026.

Project Title: Modularity of vertex operator algebras for 3d superconformal field theories and symplectic singularities

Supervisor: Dr Sven Moeller

Value of Maynooth University Doctoral Scholarship Award

The award is fully funded for four years, commencing September/October 2026 and running to completion in September 2030. The following funding is available:

• Student stipend: €25,000 per annum
• Annual Tuition Fees Support

Duration of Maynooth University Doctoral Scholarship Award

The scholarship is awarded for four years of full-time study, subject to satisfactory annual academic progression.

Project Description

Modularity of trace functions is a defining feature of 2d conformal field theories, axiomatised by vertex operator algebras (VOAs). Traditionally, VOAs with trivial associated variety were studied. Recently, exciting relations to higher-dimensional superconformal field theories and their modulispace geometry have boosted the study of VOAs whose underlying varieties are symplectic singularities. It is conjectured that trace functions of such VOAs are quasimodular forms. This project aims to prove this conjecture for a large family of VOAs, for example those coming from quiver varieties.

Mode of Study

Awardees must be resident in Ireland and available to pursue their programme of research on a full-time basis at Maynooth University for four years.

Full eligibility criteria can be found on our website.

Application and Selection Process

Please include the following in your application:

• A statement indicating why you are interested in doing a PhD in Mathematics and where your mathematical interests lie (two pages maximum)
• Curriculum Vitae
• Official University Academic Transcripts which include name, title of degree, date of conferring and the name of degree awarding body
• Non-Maynooth University applicants who are currently completing undergraduate/postgraduate programmes and have not as yet completed final exams should submit certified copies of academic transcripts with details of subjects studied and results to date
• Names and contact details of two referees
• Copy of birth certificate or valid passport English Language requirements

Applicants who are non-native speakers of the English language must provide written evidence of competency in the English language that satisfy the programme-specific requirements set out by the Maynooth University International Office.

All Maynooth University Doctoral Scholarship Awards are conditional on approval for registration by the University. All eligible candidates will be considered for open positions. Applicants may be shortlisted for interview and, if so, will be contacted directly by the Department. Late applications will not be considered.

Informal queries can be sent to Sven.Moeller@mu.ie

Closing Date: Please apply by 5pm on 12 June 2026.

Please submit applications directly to: mathsstatspg@mu.ie. Please title the subject of your email application as ‘MU Doctoral Scholarship -Sven Moeller’.