I am a Senior Lecturer in Algebra and Geometry in the Algebra and Geometry group in the Department of Mathematics and Statistics, and Assistant Dean for Engagement for the Faculty of Science and Technology, at Lancaster University.
My research is in the area of quantum algebra. Here "algebra" refers to the major branch of mathematics that studies the structure of mathematical objects and their symmetries. A brief introduction to this area - and an explanation of the various other ways the word is used - may be found in the Wikipedia article on Algebra.
The adjective "quantum" highlights a relationship with the quantum theory of physics. In the mathematics of that theory, many of the variables do not commute - that is, a times b need not equal b times a. Many of the structures in quantum algebra have a multiplication that is not commutative. The ones I study are often not far from being commutative, though. One can often deform a commutative product of two elements a and b by putting in an extra parameter, q say, and changing the product so that now ab=qba. Then ba=q-1ab and if q does not equal 1, the product is not commutative. We can think of being allowed to vary q and talk of q=1 as the "classical limit", just as classical physics can be recovered from quantum physics. The study of these deformations of well-understood classical algebraic and geometric objects is what makes up the field of quantum algebra.
More specifically, I work with Lie algebras, quantized enveloping algebras, quantized coordinate rings, partial flag varieties, cluster algebras and cluster categories. For details, please see my publications.
Previously I was Fixed-Term Fellow and Director of Studies for Mathematics at Keble College and part of the Algebra group at the Mathematical Institute, University of Oxford. I obtained my PhD from the University of London, having been based in the School of Mathematical Sciences, Queen Mary, University of London, working under the supervision of Prof. Shahn Majid.
Lecture notes for MATH225 Abstract Algebra (2019-20) are available via the link. Note that if your browser does not natively support MathML (e.g. Chrome) you may need to approve the loading of the MathJax script in order to see the mathematics rendered correctly. Feedback on the web format of these notes is welcome.
If you are interested in studying for a PhD with me beginning in October 2022, please contact me at email@example.com to discuss this. You might also like to look at the department's list of research topics in algebra and geometry.
My lecture notes from the Kent Algebra Days PGR held in July 2014 are available online, on the talks page.
For more information about this meeting, including details of the talks, the conference photo and a list of participants, please follow the above link.