research and supervision

Link to Yuri Bazlov's home page

my research interests

Representation theory

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).

Quantum algebra

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

Of particular interest to me are applications of quantum groups in Lie theory and representation theory.

Selected publications

PhD projects available

A PhD project in the area of Lie algebra actions on noncommutative rings is available from September 2024. Strong candidates with background in Lie algebras and/or noncommutative algebra should contact Yuri Bazlov if interested.

past and current projects supervised

Name Project topic Notes
PhD students
Khalil, N Hopf-Galois extensions started in 2022/23
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)
MSc/MMath/MMathPhys projects
Brennan, J Unitary reflection groups and quaternions started 2023/24
Day, H Coxeter Groups
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, from 2020)
Leach, J Topics in modern representation theory Tax analyst (Deloitte, from 2019)
Morgan, T Quantized coordinate rings PhD student (U. Montana, from 2018/19)
Christo, H Invariant theory of Coxeter groups Investment banking associate director (UBS, from 2018)
Saunders, J Topics in modern representation theory PhD (Birmingham, 2020), postdoc
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 (independent school, 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