Link to Yuri Bazlov's home page

**My research interests:**
Representation theory and quantum algebra.

- 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 arXiv.org.

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

Name | Project topic | Notes |
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PhD students |
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Ademehin, I | Lie algebra actions on noncommutative rings | started in 2015/16 |

Dold, C | Twist-equivalence of quadratic algebras associated to Coxeter groups | PhD (Manchester, 2016) |

MSc/MMath/MMathPhys projects |
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Morgan, T | Quantized coordinate rings | |

Saunders, J | Topics in modern representation theory | PhD student (Birmingham, from 2016/17) |

Reynolds, R | Quadratic algebras associated to Coxeter groups | PhD student (Edinburgh, from 2016/17) |

Green, R | Drinfeld twists in mathematical physics | PhD student (Manchester, from 2016/17) |

Holmes, N | Quasitriangular Hopf algebras arising from groups | PhD student (Southampton, from 2015/16) |

Lovatt, R | Quantum groups and quantum mechanics | Physics teacher (independent school, from 2015/16) |

McGaw, A | Hopf algebras and mystic reflection groups | PhD student (Manchester, from 2014/15) |

Webber, J | Finite group representations | PhD student (Manchester, from 2013/14) |

Henshall, C | Drinfeld twists of Nichols algebras | |

Laugwitz, R | Hopf algebras and quantum groups | DPhil (Oxon, 2015), Postdoc |