Moduli spaces of algebraic curves and mathematical physics

Supervisor(s)

Contact Dr Alexandr Buryak to discuss this project further informally.

Project description

The moduli space of curves is the space of all complex structures on a given compact two-dimensional surface. This is a complicated topological space with a very rich and interesting geometry. The moduli space of curves plays a central role in modern curve counting theories, like Gromov-Witten theory, which studies the number of algebraic curves with certain properties containing in some algebraic variety. Remarkably, the moduli space of curves also lies at the crossroad of many other mathematical disciplines, including the theory of integrable partial differential equations, differential geometry, singularity theory, combinatorics.

There are many starting points for a PhD project in this area. One can study the topological properties of the moduli space of curves, in particular, its cohomology groups. Another possibility could be to study the relations of the moduli space of curves with the theory of integrable partial differential equations. Certain differential geometric structures, related to the moduli space of curves, in particular, the Frobenius manifolds and their generalizations, could also be an object of research for a PhD project.

Entry requirements

Applicants should have, or expect to obtain, a minimum of a UK upper second class honours degree in Mathematics or a related discipline, or equivalent.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'Moduli spaces of algebraic curves and mathematical physics’ as well as Dr Alexandr Buryak as your proposed supervisor.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates.  All scholarships will be awarded on the basis of merit.

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk