Professor Jan Grabowski CMath FIMA SFHEA
Professor of AlgebraResearch Overview
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.
Web Links
Personal pages:
Research Grants
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 Sk?odowska-Curie Actions Individual Fellowship COMBGEOREP (€212,934), 2-year project, to be held by Dr Raquel Coelho Sim?es.
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.
Qualifications
December 2013: Postgraduate Certificate in Academic Practice (PGCert), 51¸£Àû.
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.
Career Details
August 2024-present: Professor of Algebra, School of Mathematical Sciences, 51¸£Àû.
August 2019-July 2024: Senior Lecturer in Pure Mathematics, School of Mathematical Sciences, 51¸£Àû.
November 2022-July 2024: Associate Dean for Engagement and Internationalisation, Faculty of Science and Technology, 51¸£Àû.
August 2020-November 2022: Assistant Dean for Engagement, Faculty of Science and Technology, 51¸£Àû.
September 2011-August 2019: Lecturer in Pure Mathematics, Department of Mathematics and Statistics, 51¸£Àû.
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.
External Roles
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
PhD Supervisions Completed
Thomas Booker-Price (October 2013-December 2017). Thesis:
Wookyung Kim (October 2020-October 2024). Thesis:
PhD Supervision Interests
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.
Selected Publications
Grabowski, J., Hindmarch, L. 5/12/2024 In: Bulletin of the London Mathematical Society. 56, 12, p. 3777-3785. 9 p.
Journal article
Grabowski, J., Hone, A., Kim, W. 28/02/2024 In: arxiv.org. 40 p.
Journal article
Cooney, N., Grabowski, J. 7/02/2020 In: arxiv.org. 7 p.
Journal article
Cooney, N., Grabowski, J.E. 15/08/2022 In: Journal of Algebra. 604, p. 296-323. 28 p.
Journal article
Grabowski, J.E., Pressland, M. 1/01/2018 In: Documenta Mathematica. 23, p. 49-76. 23 p.
Journal article
Grabowski, J.E., Gratz, S. 11/2018 In: Journal of Pure and Applied Algebra. 222, 11, p. 3395-3413. 18 p.
Journal article
Grabowski, J. 12/2015 In: Journal of Algebraic Combinatorics. 42, 4, p. 1111-1134. 24 p.
Journal article
Grabowski, J., Launois, S. 23/05/2014 In: Proceedings of the London Mathematical Society. 109, 3, p. 697-732. 36 p.
Journal article
Grabowski, J., Gratz, S., Groechenig, M. 04/2014 In: Journal of the London Mathematical Society. 89, 2, p. 337-363. 27 p.
Journal article
Allman, J.M., Grabowski, J. 06/2012 In: Journal of Algebra. 359, 1, p. 49-68. 20 p.
Journal article
Grabowski, J., Launois, S. 2011 In: International Mathematics Research Notices. 2011, 10, p. 2230-2262. 33 p.
Journal article
Grabowski, J. 2011 In: Journal of Pure and Applied Algebra. 215, 7, p. 1582-1595. 14 p.
Journal article
Grabowski, J. 14/10/2011 In: Communications in Algebra. 39, 10, p. 3491-3514. 24 p.
Journal article
Grabowski, J. 2008 In: Journal of Lie Theory. 18, 1, p. 125-140. 16 p.
Journal article
Grabowski, J. 2006 University of London.
Doctoral Thesis
Grabowski, J. 2005 In: Journal of Algebra and Its Applications. 4, 6, p. 707-737. 30 p.
Journal article
Grabowski, J. 2005 In: Pacific Journal of Mathematics. 221, 2, p. 281-301. 22 p.
Journal article
All Publications
04/01/2022 → 31/12/2022
Research
20/01/2020 → 19/01/2022
Research
01/12/2018 → 30/11/2020
Research
28/11/2014 → 27/03/2016
Research
School Engagement
Invited talk
Visiting an external academic institution
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Visiting an external academic institution
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Hosting an academic visitor
Participation in conference -Mixed Audience
Participation in conference -Mixed Audience
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Membership of committee
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Member of an organisation
Publication peer-review
Publication peer-review
Hosting an academic visitor
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Publication peer-review
Publication peer-review
Hosting an academic visitor
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Publication peer-review
Hosting an academic visitor
Invited talk
Hosting an academic visitor
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Editorial activity
Invited talk
Hosting an academic visitor
Invited talk
Membership of committee
Publication peer-review
School Engagement
Membership of committee
Publication peer-review
Membership of committee
Membership of committee
Participation in conference -Mixed Audience
Participation in conference -Mixed Audience
Publication peer-review
Participation in workshop, seminar, course
Participation in workshop, seminar, course
Hosting an academic visitor
Participation in workshop, seminar, course
Participation in conference -Mixed Audience
Algebra and Geometry
- Algebra and Geometry
- Mathematical Physics (Maths and Stats)