Link to Yuri Bazlov's home page
is a branch of mathematics concerned with the question how to “realise” abstract algebraic constructions by means of symmetries of some object (e.g., by means of linear transformations of a vector space).
is a relatively young but very active field, which includes certain directions of research in Hopf algebras, Lie theory, noncommutative ring theory, combinatorics, etc. Its scope roughly corresponds to the scope of the math.QA section of arXiv.org.
Of particular interest to me are applications of quantum groups in Lie theory and representation theory.
A PhD project in the area of Lie algebra actions on noncommutative rings is available from September 2027. See the advert. Strong candidates with background in Lie algebras, quantum groups and/or noncommutative algebra should contact Yuri Bazlov if interested.
| Name | Project topic | Notes |
|---|---|---|
| PhD students | ||
| Hull, D | started in 2026/27 | |
| Jones-Healey, E | Drinfeld twists of algebras and representations | PhD (Manchester, 2023). Mathematical consultant, Smith Institute |
| Ademehin, I | Lie algebra actions on noncommutative rings: representations in the exterior algebra of the little adjoint module | PhD (Manchester, 2020). University lecturer, Akure |
| Dold, C | Twist-equivalence of quadratic algebras associated to Coxeter groups | PhD (Manchester, 2016) |
| Selected MSc/MMath/MMathPhys projects | ||
| Beaver, E | Knot invariants and Fibonacci anyons | |
| Sharrock, T | Quantum Groups, Knot Invariants and Noncommutative Geometry | DPhil student (Oxford, from 2026/27) |
| Chen, R | Quantum Segre maps via cocycle twists | |
| Khalil, N | Hopf-Galois extensions | |
| Balada Gaggioli, L | Quantum Groups and ZX-calculus | PhD student in quantum computing |
| Font-Quer, J | The Jones polynomial via Quantum Groups | PhD student in artificial intelligence (Manchester, from 2024/25) |
| Brennan, J | Unitary reflection groups and quaternions | |
| Gibson, J | Lattices and Codes | |
| Jackson, A | The Mathematics of Error-Correcting Codes | PhD student (Durham, from 2021/22) |
| Andrews, J | Self-dual codes and invariant theory | Data Analyst (Siemens Healthineers) |
| Leach, J | Topics in modern representation theory | Tax consultant (Deloitte) |
| Morgan, T | Quantized coordinate rings | PhD student (U. Montana, from 2018/19) |
| Christo, H | Invariant theory of Coxeter groups | Investment banking director (UBS) |
| Saunders, J | Topics in modern representation theory | PhD (Birmingham, 2020), postdoc, research fellow (Bristol) |
| Reynolds, R | Quadratic algebras associated to Coxeter groups | PhD (Edinburgh, 2020), lecturer, UCL |
| Naser, A | Hopf algebras, quantum groups and the quantum double D(KS3) | Operation risk manager |
| Green, R | Drinfeld twists in mathematical physics | PhD student (Manchester, from 2016/17) |
| Holmes, N | Quasitriangular Hopf algebras arising from groups | Software engineer, James Fisher Prolec |
| Lovatt, R | Quantum groups and quantum mechanics | Physics teacher (from 2015/16) |
| Hastie, C | Non-trivial invariant Drinfeld twists on the group Hopf algebra over the symmetric group | Analytics consultant, InterWorks |
| McGaw, A | Hopf algebras and mystic reflection groups | PhD (Manchester, 2018). Teacher of Mathematics |
| Henshall, C | Cocycle twists of Nichols algebras | Big data expert, Lloyds Group |
| Webber, J | Finite group representations | PhD (Manchester, 2018). Assistant professor, Harvard University |
| Anderson, J | Hopf algebra deformation through the Drinfeld twist | Software engineer, Cisco |
| Laugwitz, R | Hopf algebras and quantum groups | DPhil (Oxon, 2015). University lecturer, Nottingham |