I am currently supervising two PhD students in Edinburgh:
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.
My former students in Edinburgh are
Vivek Mistry, 2018-2022, PhD thesis "Donaldson-Thomas theory and cohomological Hall algebras of character stacks"
Sebastian Schlegel Mejia 2019-2023, PhD thesis "BPS cohomology for 2-Calabi-Yau categories"
At the University of Glasgow I also acted as co-supervisor to Okke van Garderen, 2017-2021, PhD thesis "Donaldson–Thomas invariants of threefold flops"
I may be taking on one student in October 2025, through the Centre for Doctoral Training in Algebra, Geometry and Quantum Fields. 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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