Dr Jan Grabowski FIMA SFHEA
Senior Lecturer in Algebra and GeometryProfessional Role
Associate Dean for Engagement and Internationalisation, Faculty of Science and Technology
Research 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: https://www.maths.lancs.ac.uk/~grabowsj/
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 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.
Qualifications
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.
Career Details
August 2020-November 2022: Assistant Dean for Engagement, Faculty of Science and Technology, Lancaster University.
August 2019-November 2022: Senior Lecturer in Pure Mathematics, Department of Mathematics and Statistics, 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.
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: Applications of Graded Methods to Cluster Variables in Arbitrary Types
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
Automorphism groupoids in noncommutative projective geometry
Cooney, N., Grabowski, J.E. 15/08/2022 In: Journal of Algebra. 604, p. 296-323. 28 p.
Journal article
Graded Frobenius cluster categories
Grabowski, J.E., Pressland, M. 1/01/2018 In: Documenta Mathematica. 23, p. 49-76. 23 p.
Journal article
Graded quantum cluster algebras of infinite rank as colimits
Grabowski, J.E., Gratz, S. 11/2018 In: Journal of Pure and Applied Algebra. 222, 11, p. 3395-3413. 18 p.
Journal article
Graded cluster algebras
Grabowski, J. 12/2015 In: Journal of Algebraic Combinatorics. 42, 4, p. 1111-1134. 24 p.
Journal article
Graded quantum cluster algebras and an application to quantum Grassmannians
Grabowski, J., Launois, S. 23/05/2014 In: Proceedings of the London Mathematical Society. 109, 3, p. 697-732. 36 p.
Journal article
Cluster algebras of infinite rank
Grabowski, J., Gratz, S., Groechenig, M. 04/2014 In: Journal of the London Mathematical Society. 89, 2, p. 337-363. 27 p.
Journal article
A quantum analogue of the dihedral action on Grassmannians
Allman, J.M., Grabowski, J. 06/2012 In: Journal of Algebra. 359, 1, p. 49-68. 20 p.
Journal article
Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases
Grabowski, J., Launois, S. 2011 In: International Mathematics Research Notices. 2011, 10, p. 2230-2262. 33 p.
Journal article
Examples of quantum cluster algebras associated to partial flag varieties
Grabowski, J. 2011 In: Journal of Pure and Applied Algebra. 215, 7, p. 1582-1595. 14 p.
Journal article
Braided enveloping algebras associated to quantum parabolic subalgebras
Grabowski, J. 14/10/2011 In: Communications in Algebra. 39, 10, p. 3491-3514. 24 p.
Journal article
Braided Lie bialgebras associated to Kac-Moody algebras
Grabowski, J. 2008 In: Journal of Lie Theory. 18, 1, p. 125-140. 16 p.
Journal article
Inductive constructions for Lie bialgebras and Hopf algebras
Grabowski, J. 2006 University of London.
Doctoral Thesis
On Lie induction and the exceptional series
Grabowski, J. 2005 In: Journal of Algebra and Its Applications. 4, 6, p. 707-737. 30 p.
Journal article
A triple construction for Lie bialgebras
Grabowski, J. 2005 In: Pacific Journal of Mathematics. 221, 2, p. 281-301. 22 p.
Journal article
All Publications
Schubert Calculus via Cluster Categories
04/01/2022 → 31/12/2022
Research
Combinatorial and Geometric Methods in Representation Theory
20/01/2020 → 19/01/2022
Research
Supplementary Issue of Glasgow Mathematical Journal on Non-Associative Algebras
01/12/2018 → 30/11/2020
Research
Reconstructing Broken Symmetry
28/11/2014 → 27/03/2016
Research
UKRI Talent Peer Review College (External organisation)
Membership of committee
Aarhus University
Visiting an external academic institution
Geometric and Homological Methods in Representation Theory
Participation in conference -Mixed Audience
Sira Gratz
Hosting an academic visitor
Non-associative algebras
Participation in conference -Mixed Audience
Quantum homogeneous spaces
Participation in conference -Mixed Audience
MAXIMALS seminar
Invited talk
University of York (External organisation)
Membership of committee
Algebra seminar
Invited talk
Carnegie Trust for the Universities of Scotland (External organisation)
Member of an organisation
Proceedings of the London Mathematical Society (Journal)
Publication peer-review
Journal of Algebra (Journal)
Publication peer-review
Charlie Beil
Hosting an academic visitor
Algebra and Geometry seminar
Invited talk
Algebras and Representation Theory (Journal)
Publication peer-review
Algebra seminar
Invited talk
Algebra seminar
Invited talk
Advances in Mathematics (Journal)
Publication peer-review
Algebra seminar
Invited talk
London Algebra Colloquium
Invited talk
London Mathematical Society Lecture Note Series (Journal)
Publication peer-review
Journal of Algebra (Journal)
Publication peer-review
Advances in Applied Mathematics (Journal)
Publication peer-review
Sian Fryer
Hosting an academic visitor
Algebra-Geometry seminar
Invited talk
Algebras and Representation Theory (Journal)
Publication peer-review
Matthew Pressland
Hosting an academic visitor
Invited talk at Special Session on "Combinatorics and Geometry of Quantum Algebras".
Invited talk
Sian Fryer
Hosting an academic visitor
Invited talk at LMS Workshop on Cluster Algebras and Preprojective Algebras, Cardiff University
Invited talk
4 lectures at instructional course "Kent Algebra Days PGR"
Invited talk
Oberseminar zur Algebra und Algebraischen Kombinatorik
Invited talk
Pure Mathematics Colloquium
Invited talk
London Algebra Colloquium
Invited talk
Invited talk at conference "Cluster algebras and combinatorics", University of Münster
Invited talk
Glasgow Mathematical Journal (Journal)
Editorial activity
Algebra-Geometry seminar, Newcastle University
Invited talk
Launois Stéphane
Hosting an academic visitor
Pure Mathematics seminar, University of Leicester
Invited talk
Engineering and Physical Sciences Research Council (External organisation)
Membership of committee
Journal of the London Mathematical Society (Journal)
Publication peer-review
STEMNET (Science, Technology, Engineering and Mathematics Network)
School Engagement
Engineering and Physical Sciences Research Council (External organisation)
Membership of committee
Journal of Algebra (Journal)
Publication peer-review
Netherlands Organisation for Scientific Research - NWO (External organisation)
Membership of committee
Engineering and Physical Sciences Research Council (External organisation)
Membership of committee
Future directions for quantum groups
Participation in conference -Mixed Audience
XV International Conference on Representations of Algebras (ICRA XV)
Participation in conference -Mixed Audience
Algebras and Representation Theory (Journal)
Publication peer-review
Algebra seminar, University of Glasgow
Participation in workshop, seminar, course
Pure Mathematics seminar, Lancaster University
Participation in workshop, seminar, course
Sira Gratz
Hosting an academic visitor
29th meeting of ARTIN (Algebra and Representation Theory in the North)
Participation in workshop, seminar, course
Kent Algebra Days 2011
Participation in conference -Mixed Audience
Algebra and Geometry
Algebra and Geometry
- Algebra and Geometry
- Mathematical Physics (Maths and Stats)