Dr Jan Grabowski

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: http://www.maths.lancaster.ac.uk/~grabowsj

Research Grants

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

January 2014: Faculty Travel Grant (£282), to fund attendance at meeting "Cluster algebras and combinatorics", February 2014, Münster, Germany.

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.

November 2011: Faculty Travel Grant (£348), to fund attendance at British Mathematical Colloquium, April 2012, Canterbury, Kent.

October 2011: Departmental Research Incentivisation Grant (£550), to fund research visit of Sira Gratz to Lancaster University.

Current Teaching

MATH112 Discrete Mathematics

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

September 2011-present: 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.

Professional Role

Outreach Officer, Department of Mathematics and Statistics (September 2011-present)

Chair of Publicity, Web and Outreach Committee, Department of Mathematics and Statistics (September 2012-present)

Member of Faculty of Science and Technology Marketing Committee (October 2012-present)

Member of University Web User Group (previously Project Orpheus User Group) (October 2012-present)

Deputy Admissions Tutor, Department of Mathematics and Statistics (September 2011-August 2014)

External Roles

Subject Editor (Algebra), Glasgow Mathematical Journal

Member of EPSRC Peer Review College

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