Supervision

I am currently supervising four PhD students in Edinburgh:

• Vivek Mistry, who started in October 2018, and is working on motivic DT invariants and cohomological Hall algebras associated to representations of fundamental groups of Riemann surfaces

• Sebastian Schlegel Mejia, who started in October 2019 and is working on cohomological Hall algebras and BM homology of stacks of Higgs bundles

• Sarunas Kaubrys (joint with Pavel Safronov), who started in October 2021, and is working on cohomological DT theory associated to representations of fundamental groups of real 3-manifolds

• Shivang Jindal, who started in October 2021, and is working on geometric representation theory and critical cohomology of Hilbert schemes of threefolds.

I may be taking on one student in October 2023. Potential applicants are encouraged to take a look at my research page to get an idea of the range of things that I work on, or drop me an email if they'd like to know more. There are many projects we could try out, including, but not limited to

• Working out BPS Lie algebras for flopping curves: This is an investigation that combines the very new (BPS Lie algebras) with the rather old (but great!): birational geometry of threefold flopping contractions.

• Stable envelopes and Higgs bundles: again combining brand new gadgets in algebraic/symplectic geometry with rather classical ones.

• Coloured box counting: Incredibly, there are still a lot of questions we can't answer regarding coloured 3d partitions, despite the problems being easy to state and approachable from lots of areas of maths, like toric geometry, representation theory and combinatorics.

• Quantum groups from geometry. Via various approaches, there is a way to build "quantum-group-like" objects directly out of geometry, as opposed to realising familiar quantum groups via geometric means. One can approach these objects via specific examples, before shooting for general structure results.

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