Research opportunities

I have projects for prospective MSc students and PhD students. This would be in any of the areas of gauge theory, the moduli space of Riemann surfaces and related moduli spaces, applications of algebraic geometry to integrable systems and various mathematical physics related problems.

Project topics:
Super Riemann surfaces Reading: arxiv:1209.2459
Topological recursion; Quantum curves Reading: arxiv:0811.3531 arxiv:1502.04394
Moduli space of flat connections; representation theory; Verlinde formula; conformal foeld theory Reading: arxiv:0210466
Differentials on Riemann surfaces applied to gauge theory Reading: arxiv:0306238 arxiv:0601062
Quantum Teichmueller theory; moduli space of hyperbolic surfaces; cluster algebras Reading: arxiv:1107.5069

I currently supervise the following PhD students.
Lukas Anagnostou works on the moduli space of super Riemann surfaces.
Michael Swaddle works on the Kontsevich-Soibelman construction of topological recursion.

Past PhD students.
Wee Chaimanowong Seiberg-Witten Theory and Topological Recursion (2020).
Oliver Leigh Enumerative problems in algebraic geometry motivated from physics (2019).
Joe Chan On hyperbolic monopoles (2017).
Yi Huang Moduli spaces of surfaces (2014).
Callum Sleigh Eynard-Orantin theory of the A-polynomial (2013).
Nick Scott Polynomial hierarchies generated by Eynard-Orantin invariants (2012).
Norman Do Intersection theory on moduli spaces of curves via hyperbolic geometry (2010).
Thomas Handscomb Characteristic classes of surface bundles and Lefschetz fibrations (2009).

PhD at Melbourne

Vacation Scholarships