Partition functions through the lens of topological recursion

The proposed research aims to resolve longstanding conjectures, prove rigorous results, and introduce new structures concerning partition functions that have arisen from mathematical physics. The rapidly developing theory of topological recursion will be used as an illuminating and unifying lens. This perspective allows for novel approaches to mathematical problems motivated by the physics of quantum gravity, string theory, and mirror symmetry.

At the moment, rigorous mathematical results significantly lag behind the predictions stemming from physics and the current proposal seeks to redress this disparity. A major theme and innovation underlying the research is to construct partition functions by gluing together certain elementary partition functions. The project will lead to significant advancement of our understanding of enumerative geometry and quantum invariants, as well as new connections between these concepts.

ROLE DESCRIPTION

The PhD student will work closely with Associate Professor Norm Do to perform a relevant literature review, compute enumerative invariants captured by the partition functions of interest, and develop the required techniques to tackle unsolved problems in the topic of the project. They will be expected to collaborate on research publications to disseminate the new discoveries stemming from the research.

SKILLS AND EXPERIENCE

• An Honours degree, Master’s degree, or equivalent, in mathematics is required, involving a thesis whose topic lies in pure mathematics.

• Strong foundations in pure mathematics – algebra, analysis, combinatorics, geometry and topology – are essential. Previous studies in physics are not essential, although preference may be given to candidates who have some physics background.

• Applicants for whom English is not their first language may be required to demonstrate their English language proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 6.0 in each component.

EXPECTED START DATE

The PhD student is expected to start between 1 February and 1 August.

FURTHER INFORMATION

Enquiries and applications should be sent to Associate Professor Norm Do ([email protected]) and must be received by Friday 6 December 2024.

Applications should include a cover letter, a curriculum vitae, an academic transcript, and a list of referees from whom recommendation letters may be requested. Applicants are welcome to also attach a copy of their Honours and/or Master’s thesis.

Applicants may be asked to participate in an online interview and to submit their response to a mathematical task to assess their suitability for the project.

Further details on the School of Mathematics at Monash University and its graduate program can be found at the following website.

https://www.monash.edu/science/schools/school-of-mathematics/postgraduate-research