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.  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=(1/q)ab 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 and quantum cluster algebras.

I am currently offering PhD projects in three areas: 1. Quantum groups, including producing novel quantum groups from the double bosonisation construction. 2. Cluster algebras, their quantizations and representation theory. 3. Relationships with mathematical physics, including Verlinde algebras, quantum cohomology and integrable systems and their relationships to quantum cluster algebras.

Personal pages: https://www.maths.lancs.ac.uk/~grabowsj/

January 2022: Principal Investigator on EPSRC Small Grant EP/W017881/1 (£33,573), 12-month project entitled "Schubert calculus via cluster categories".

January 2020: Principal Investigator on Marie Skłodowska-Curie Actions Individual Fellowship COMBGEOREP (€212,934), 2-year project, to be held by Dr Raquel Coelho Simões.

October 2014: EPSRC First Grant EP/M001148/1 (£98,663), 16-month project entitled "Reconstructing broken symmetry".

February 2012: London Mathematical Society Scheme 1 Conference Grant (£2,567.80), to part-fund conference "Future directions for quantum groups" held in Lancaster in September 2012.

February 2012: Faculty Research Grant (£1,000), to part-fund conference "Future directions for quantum groups" held in Lancaster in September 2012.

December 2013: Postgraduate Certificate in Academic Practice (PGCert), Lancaster University.

April 2006: PhD in Mathematics, Queen Mary, University of London, under the supervision of Prof. Shahn Majid.

July 2002: Master of Mathematics with Honours (MMath(Hons)), First class, University of Warwick.

August 2024-present: Professor of Algebra, School of Mathematical Sciences, Lancaster University.

August 2019-July 2024: Senior Lecturer in Pure Mathematics, School of Mathematical Sciences, Lancaster University.

November 2022-July 2024: Associate Dean for Engagement and Internationalisation, Faculty of Science and Technology, Lancaster University.

August 2020-November 2022: Assistant Dean for Engagement, Faculty of Science and Technology, Lancaster University.

September 2011-August 2019: Lecturer in Pure Mathematics, Department of Mathematics and Statistics, Lancaster University.

October 2009-September 2011: Fixed-Term Fellow by Special Election in Mathematics, Keble College, Oxford.

October 2008-October 2009: Stipendiary Lecturer in Mathematics, Keble College, Oxford.

January-March 2008-2010: Lecturer and class tutor, Mathematical Institute, Oxford.

October 2005-September 2008: Research Fellow and Tutor in Mathematics, Keble College, Oxford.

Subject Editor (Algebra), Glasgow Mathematical Journal

Member of EPSRC Peer Review College

Member of UKRI Talent Peer Review College

Carnegie Research Assessor, Carnegie Trust for the Universities of Scotland

External Examiner, Newcastle University

Thomas Booker-Price (October 2013-December 2017). Thesis: Applications of Graded Methods to Cluster Variables in Arbitrary Types

Wookyung Kim (October 2020-October 2024). Thesis: Discrete integrable systems associated with deformations of cluster maps