Curriculum Vitae for Jan E. Grabowski

Contact details

Address:
Department of Mathematics and Statistics,
Fylde College,
Lancaster University,
Lancaster,
LA1 4YF
United Kingdom
Office:
B66, Fylde College
Telephone:
+44 (0)1524 594317
Fax:
+44 (0)1524 592681
Email:
j.grabowski@lancaster.ac.uk
Website:
http://www.maths.lancs.ac.uk/~grabowsj/

Research

Employment

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.
October 2005-September 2008
Lecturer in Mathematics, Somerville College, Oxford.

Qualifications

December 2013
Postgraduate Certificate in Academic Practice (PGCert), Lancaster University.
April 2006
PhD in Mathematics, Queen Mary, University of London (QMUL), under the supervision of Prof. Shahn Majid.
July 2002
Master of Mathematics with Honours (MMath(Hons)), First class, University of Warwick.

Publications

  1. A triple construction for Lie bialgebras, Pacific Journal of Mathematics, 221, no. 2 (2005): 281-301, arXiv:math.QA/0312507
  2. On Lie induction and the exceptional series, Journal of Algebra and Its Applications, 4, no. 6 (2005): 707-737, Special Issue on Representation Theory and Its Applications, arXiv:math.QA/0409359.
  3. Braided-Lie bialgebras associated to Kac-Moody algebras, Journal of Lie Theory, 18, no. 1 (2008): 125-140, arXiv:0708.4200.
  4. Examples of quantum cluster algebras associated to partial flag varieties, Journal of Pure and Applied Algebra, 215 (2011): 1582-1595, arXiv:0907.4922.
  5. with Stéphane Launois. Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases, International Mathematics Research Notices, 10 (2011): 2230-2262, arXiv:0912.4397.
  6. Braided enveloping algebras associated to quantum parabolic subalgebras, Communications in Algebra, 39, no. 10 (2011): 3491-3514, arXiv:0706.0455.
  7. with Justin Allman. A quantum analogue of the dihedral action on Grassmannians, Journal of Algebra, 359 (2012): 49-68, arXiv:1102.0422.
  8. with Sira Gratz. Cluster algebras of infinite rank, with an appendix by Michael Groechenig, Journal of the London Mathematical Society, 89, no. 2 (2014): 337-363, arXiv:1212.3528.
  9. with Stéphane Launois. Graded quantum cluster algebras and an application to quantum Grassmannians, Proceedings of the London Mathematical Socity, 109, no. 3 (2014): 697-732, arXiv:1301.2133.
  10. Graded cluster algebras, Journal of Algebraic Combinatorics, 42, no. 4 (2015): 1111-1134, arXiv:1309.6170.
  11. with Sira Gratz. Graded quantum cluster algebras of infinite rank as colimits, Journal of Pure and Applied Algebra, to appear, arXiv:1510.04109.
  12. with Matthew Pressland. Graded Frobenius cluster categories, Documenta Mathematica, to appear, arXiv:1609.09670.

Research description and interests

My research is concerned with the algebraic structures related to quantum groups and noncommutative geometry. These include Hopf algebras and Lie bialgebras and are especially important for their links to the study of the Yang-Baxter equation, also known as the braid relations. I have studied inductive constructions for Lie bialgebras and Hopf algebras based on the addition of nodes to Dynkin diagrams and their implications for the classification of simple Lie algebras and other structural questions. More recently, I have examined quantum cluster algebra structures associated to partial flag varieties. These structures encode much of the intricate combinatorics related to the algebraic geometry of these varieties.

Collaborations and supervision

September 2015-present
Working with Matthew Pressland, Max-Planck-Institut für Mathematik, Bonn.
December 2014-present
Working with Nicholas Cooney, Université Blaise Pascal - Clermont-Ferrand II.
October 2013-present
Supervision of PhD student Thomas Booker-Price.
May 2011-July 2011
Supervised visiting student Paul Schneider, ENS Cachan, France.
October 2010-present
Working with Sira Gratz, Leibniz Universität Hannover, Germany. (Supervised Masters thesis October 2010-July 2011.)
May 2010-November 2011
Worked with Justin Allman, University of North Carolina at Chapel Hill, USA.
June 2009-present
Working with Stéphane Launois, University of Kent.

Other research activity

March 2017
Hosted Charlie Beil for research visit to Lancaster University.
September 2015
Hosted Matthew Pressland for research visit to Lancaster University.
February 2015, March 2016
Hosted Sian Fryer for research visits to Lancaster University.
June 2014
3-day research visit to work with Sira Gratz at the Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Germany.
October 2013
Hosted Stéphane Launois for three-day research visit to Lancaster University.
November 2011
Hosted Sira Gratz for four-day research visit to Lancaster University, funded by Departmental Research Incentivisation Award.
June 2009
Visit to work with Stéphane Launois at the University of Kent.
Summer 2001
Research Project entitled "Orthogonal representations of generalisations of the Temperley-Lieb algebras", supported by a Nuffield Foundation Undergraduate Research Bursary, under the supervision of Dr. Bruce Westbury, University of Warwick.

Research grants

November 2014
Principal Investigator on EPSRC First Grant EP/M001148/1 (£98,663), 16-month project entitled "Reconstructing broken symmetry".
October 2014
Co-Investigator on EPSRC Standard Grant EP/M017001/1 (£6,367), part-funding for Workshop on Homotopical Algebra and Geometry, to be held at Lancaster in April 2015.
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.

Thesis examinations

July 2015
Internal Examiner of PhD thesis of Heather Johnson, Lancaster University.
July 2011
Examiner of Masters thesis of Sira Gratz, ETH Zürich.

Communication

Invited seminar and network meeting presentations

February 2017
Algebra and Geometry seminar, School of Mathematics, University of Bristol.
January 2017
Algebra seminar, Department of Mathematics, University of York.
November 2016
Algebra seminar, Mathematical Institute, Oxford.
October 2016
Algebra seminar, University of Kent.
October 2016
London Algebra Colloquium, Department of Mathematics, City University London.
March 2016
Pure Mathematics seminar, Department of Mathematics and Statistics, Lancaster University.
March 2016
Algebra-Geometry seminar, School of Mathematics and Statistics, Newcastle University.
March 2015
Pure Mathematics Colloquium, School of Mathematics and Statistics, University of Sheffield.
February 2015
67th Bristol-Leicester-Oxford Colloquium (BLOC), City University, London.
Janaury 2015
Algebra seminar, Department of Pure Mathematics, University of Leeds.
June 2014
Oberseminar zur Algebra und Algebraischen Kombinatorik, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Germany.
April 2014
Pure Mathematics Colloquium, Department of Mathematical Sciences, Durham University.
March 2014
London Algebra Colloquium, Queen Mary, University of London.
November 2013
"Gradings on cluster algebras and associated combinatorics", Algebra-Geometry Seminar, School of Mathematics and Statistics, Newcastle University.
October 2013
"Gradings on cluster algebras and associated combinatorics", Pure Mathematics Seminar, Department of Mathematics, University of Leicester.
November 2011
"Quantizing cluster algebras associated to coordinate rings", Algebra seminar, University of Glasgow.
November 2011
"A dihedral group action on Grassmannians and its quantization", Pure Mathematics seminar, Lancaster University.
October 2011
"Some properties of quantum Grassmannians", ARTIN, Newcastle University.
May 2011
"Some quantum analogues of properties of Grassmannians", MAXIMALS, University of Edinburgh.
November 2010
"An introduction to cluster algebras and their quantum analogues", Mathematics seminar, University of Kent.
October 2010
"Quantizing Grassmannians, Schubert cells and cluster algebras", Algebra seminar, University of Manchester.
May 2009
"Partial flag varieties and quantum cluster algebras", Algebra and Geometry seminar, University of Bristol.
March 2009
"Partial flag varieties and quantum cluster algebras", 44th Bristol-Leicester-Oxford Colloquium (BLOC), University of Leicester.
November 2008
"Cluster algebras, partial flag varieties and quantum groups", London Algebra Colloquium.
April 2008
"Making modules into algebras", Mathematics research seminar, City University, London.
March 2008
"Making modules into algebras", Pure and Applied Mathematics seminar, University of Kent.
September 2007
"Some algebras associated to quantum parabolic subalgebras", Algebra seminar, University of Leeds.
January 2004
"Lie bialgebras and Lie induction", Topology and Geometry seminar, National University of Singapore.
December 2004
"On Lie induction and the exceptional series", Séminaire sur les Algèbres Enveloppantes, Institut de Máthematiques de Jussieu, Paris.

Also several talks to the Quantum Groups seminar at Queen Mary and the Representation Theory seminar, Kinderseminar and to the Invariants Society at Oxford.

Conferences

June 2015
Special Session on "Combinatorics and Geometry of Quantum Algebras", International Meeting of the American, European and Portuguese Mathematical Societies, Porto, Portugal.
Invited talk "Recovering automorphisms of quantum spaces".
March 2015
"Algebraic Interfaces of Integrability", Workshop on Classical and Quantum Integrability, University of Leeds.
Invited talk "Clusters, combinatorics, grading, twisting and quantization".
October 2014
LMS Workshop on Cluster Algebras and Preprojective Algebras, School of Mathematics, Cardiff University.
Invited talk "Quantizing cluster algebra constructions".
February 2014
"Cluster algebras and combinatorics", Mathematical Institute, University of Münster, Germany.
Gave invited talk "Graded cluster algebras and quantum Grassmannians".
September 2013
"Mirror Symmetry and Cluster Algebras", School of Mathematics, University of Leeds.
Presented poster "Graded cluster algebras".
August 2012
XV International Conference on Representations of Algebras and Workshop (ICRA XV), Universität Bielefeld, Germany.
Gave talk entitled "A quantum analogue of a dihedral group action on Grassmannians".
August 2011
Kent Algebra Days 2011, University of Kent.
Gave invited talk entitled "Quantum cluster algebras: a survey".
December 2009
2nd Belgian and London Mathematical Societies Conference, Katholieke Universiteit Leuven, Belgium.
Gave invited talk entitled "Quantizing Grassmannians, Schubert cells and cluster algebras".
June 2009
Geometric Representation Theory and Extended Affine Lie Algebras, University of Ottawa, Ontario, Canada.
Presented poster "Examples of quantum cluster algebras associated to partial flag varieties".
March 2009
Algebraic Lie Structures with Origins in Physics, Isaac Newton Institute for Mathematical Sciences, Cambridge.
Presented poster "Braided enveloping algebras and quantum cluster algebras related to partial flag varieties".
January 2008
LieGrits workshop, Mathematical Institute, University of Oxford.
August 2007
XII International Conference on Representations of Algebras and Workshop (ICRA XII), Nicolaus Copernicus University, Toruń, Poland.
Gave 20 minute talk entitled "On the inductive construction of quantized enveloping algebras".
June 2007
Workshop on Cherednik Algebras, International Centre for Mathematical Sciences (ICMS), Edinburgh.
December 2006
Trends in Noncommutative Geometry, Isaac Newton Institute for Mathematical Sciences, Cambridge.
June 2005
Algebraic Groups and Finite Reductive Groups, École Polytechnique Fédérale de Lausanne, Switzerland.
May 2005
Algebras and Representation Theory, Symposium on Noncommutative Algebra and its Applications, University of Warwick.
June 2004
Fourth European Congress of Mathematics, Stockholm, Sweden.
June 2004
Representation Theory and its Applications, Uppsala University, Sweden.
Gave 25 minute talk entitled "Lie induction: constructing Lie bialgebras".
November 2003
LMS Workshop on Contemporary Aspects of Mathematical Physics and Regional Meeting, Gregynog Hall, Wales.
Presented poster "Fuss-Catalan recoupling theory".
April 2002
B(A)MC, University of Warwick.

In addition, I have chaired sessions at

Network meetings

I have attended meetings of the ABC-KLM Network, taken part in the LMS Workshop series on Quantum Groups and Noncommutative Geometry (two one-day meetings) and meetings of BLOC (Bristol-Leicester-Oxford Colloquium). I spoke at a meeting of ARTIN (Algebra and Representation Theory in the North) in October 2011.

Instructional courses

Given

January-June 2015
Led Derived Categories Reading Group, Lancaster. Topics including representations of quivers, derived categories of these and derived categories of coherent sheaves on varieties.
July 2014
Cluster algebras and their quantum analogues (4 lectures), Kent Algebra Days PGR, University of Kent.

Attended

September 2004
Noncommutative spaces: their topology and measure theory, LMS/EPSRC Short Course, University of Southampton.
September 2003
Derived Categories in Algebra and Geometry, LMS/EPSRC Short Course, University of Warwick.

Professional training

November 2015
Attended 2-day residential course "Communication and Media Skills", Royal Society at Chicheley Hall.
October 2012-2013
Completed Certificate in Academic Practice, Lancaster University.
May 2012
Attended course "Supervising Research Students", Lancaster University.
November 2011
Attended course "Using Audio Visual Equipment in Lecture Theatres" and completed online modules "Diverstiy in the workplace" and "Information security", Lancaster University.
November 2011
Attended course "Welcome to Lancaster", Lancaster University. (0.5 days)
Spring 2008
Completed programme on "Developing Teaching and Learning" (reading seminar and submission of portfolio), University of Oxford.
May 2007
Workshops on "Planning Lectures" and "Delivering a Course of Lectures", University of Oxford. (Two 3-hour sessions)
October 2005
Attended course "Introduction to Academic Practice", University of Oxford. (3 days)
November 2004
UK Research Councils' GRADSchool, Brighton. (3 days)

Conference organisation

Organiser of 49th ARTIN (Algebra and Representation Theory in the North) network meeting in Lancaster in November 2016.

Organised 3-day meeting entitled "Future directions for quantum groups", held in Lancaster in September 2012. Funded by grants from the London Mathematical Society and the Faculty of Science and Technology, Lancaster University.

Co-organiser of 5-day LMS 150th Anniversary Northern Regional Meeting and Workshop on Homotopical Algebra, held in Lancaster in April 2015. Funded by grants from the London Mathematical Society and the EPSRC.

Professional membership and activities

Subject Editor (Algebra) for the Glasgow Mathematical Journal.
Member of the EPSRC Peer Review College (from September 2013, renewed September 2016).
Referee for Advances in Mathematics, the Journal of Algebraic Combinatorics, Frontiers of Mathematics in China, Algebras and Representation Theory (2), the Journal of Algebra (2), the Journal of the London Mathematical Society (2) and Advances in Applied Mathematics.
Reviewer of research proposals for EPSRC, FQRNT (Le fonds québécois de la recherche sur la nature et les technologies, Canada) and NWO (De Nederlandse Organisatie voor Wetenschappelijk Onderzoek; Netherlands Organistion for Scientific Research).
Reviewer for Mathematical Reviews and Zentralblatt.
Member, London Mathematical Society.
Member, European Mathematical Society.
Fellow of the Higher Education Academy (from December 2013); previously Associate Fellow (from July 2008).

Teaching and administration

Teaching experience

2015-2017
Lecturing and workshop tutoring for MATH112 Discrete Mathematics and MATH225b Rings.
2014-2015
Lecturing and workshop tutoring for MATH112 Discrete Mathematics.
2011-2015
Supervision of MATH390 Group Project and MATH491 Pure Mathematics Dissertation students.
2013-2014
Lecturing and workshop tutoring for MATH112 Discrete Mathematics and MATH225b Rings.
2012-2013
Lecturing and workshop tutoring for MATH112 Discrete Mathematics, MATH328 Number Theory and MATH225b Rings.
2011-2012
Lectured MATH328 Number Theory and MATH114 Discrete Mathematics and workshops for module MATH110.
January-March 2008-2010
Lecturer for third year course "Group Theory", Mathematical Institute, Oxford. Also class tutor for same.
October 2005-present
Tutorial teaching of first and second year undergraduates, Keble College and Somerville College, Oxford.
Courses taught:
October 2006-April 2007
Tutor for one-term course entitled "Number Theory" for students on exchange programme between Exeter College, Oxford and Williams College, MA, USA (two groups: two students and one student).
March 2005
Waltham Forest AimHigher masterclass for year 10 students, entitled "What is a number?"
October 2004-April 2005
Undergraduate exercise classes (average: 30 students), QMUL.
October 2002-April 2005
Undergraduate coursework marking and administration, QMUL.
October 2002-July 2003
Private one-to-one tuition, A-level and GCSE.
October 2001-June 2002
First year undergraduate mathematics supervision tutor, University of Warwick. Small group teaching (four students) and marking for core first year courses.

Teaching prizes

July 2008
Departmental Teaching Development Award, Mathematical Institute, Oxford.

Teaching development activities

October 2015
Gave talk "What does that mean, precisely?" - learning to work with definitions and led discussions at departmental Teaching and Learning sharing practice event.
July 2015
Talk "What does that mean, precisely?" - learning to work with definitions, Transition in year 1: Opportunities and challenges, Sharing Practice Day 2015, Lancaster University.
December 2013
Completed Postgraduate Certificate in Academic Practice (PGCert), Lancaster University.

Undergraduate admissions experience

September 2011-2014
Deputy Admissions Tutor, Department of Mathematics and Statistics, Lancaster University.
December 2005-2010
Admissions interviewing, Keble College, Oxford.
September 2003 & 2004
Clearing assistant, QMUL.

Outreach and engagement activties

May 2013-present
STEM Ambassador.
September 2011-July 2016
Outreach Officer, Department of Mathematics and Statistics, Lancaster University.

Administrative responsibilities

September 2016-present
Part I Director of Studies (shared).
March 2015-present
Chair of university-level Web User Group, member of Web Transformation Steering Group.
October 2012-March 2015
Member of Web User Group.
September 2012-present
Chair of Publicity, Web and Outreach Committee, Department of Mathematics and Statistics, Lancaster University.
April 2010-September 2011
Director of Studies for Mathematics, Keble College, Oxford.
October 2009-11
Member, Domestic Committee, Keble College, Oxford.
October 2007-08
Member, Finance Committee, Keble College, Oxford.
May 2006-August 2006
Acting Senior Mathematics Tutor, Keble College, Oxford.