Homepage for Laurence Barker

Group representation theorist, Associate Professor in the Department of Mathematics at Bilkent University.



Main research interests

Finite symmetries, that is to say, finite group theory. In particular,  finite group representation theory. Especially applications of group functors to finite group representation theory. I also have an occasional interest in applications of finite group representation theory to discrete methods in engineering and physics.


L. Barker, I. Tuvay, Real representation spheres and the real monomial Burnside ring, J. Algebra 353, 79-92 (2012). realrevised.pdf

L. Barker, Tornehave morphisms I: resurrecting the virtual permutation sets annihilated by linearization, Communications in Algebra 39, 355-395 (2011). tornehave1rev.pdf

L. Barker, Tornehave morphisms II: the lifted Tornehave morphism and the dual of the Burnside functor, J. Pure and Applied Algebra 214, 1759-1777 (2010). tornehave2rev.pdf

L. Barker, Rhetorical biset functors, rational p-biset functors and their semisimplicity in characteristic zero, J. Algebra 319, 3810-3853 (2008). semisim_preprint.pdf

L. Barker, Genotypes of irreducible representations of finite p-groups, J. Algebra, 306, 655-681 (2007). genetic_preprint.pdf

L. Barker, Fibred permutation sets and the idempotents and units of monomial Burnside rings, J. Algebra 281, 535-566 (2004).

L. Barker, E. Yalcin, A new notion of rank for finite supersolvable groups and free linear actions on products of spheres, J. Group Theory 6, 347-364 (2003).

L. Barker, Continuum quantum systems as limits of discrete quantum systems. IV. Affine Canonical Transforms, J. Math. Phys. 44, 1535-1553 (2003).

L. Barker, Continuum quantum systems as limits of discrete quantum systems. III. Operators, J. Math. Phys. 42 (10), 4652-4668 (2001) .

L. Barker, Continuum quantum systems as limits of discrete quantum systems, II: state functions, J. Phys. A: Math. Gen. 22, 4673-4682 (2001).

L. Barker, Continuum quantum systems as limits of discrete quantum systems. I: state vectors, J. Functional Analysis 186, 153-166 (2001).

L. Barker, C. Candan, M. A. Kutay, T. Hakioglu, H. Ozaktas, The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform, J. Phys. A: Math. Gen. 33, 2209-2222 (2000).

L. Barker, The discrete fractional Fourier transform and Harper's equation, Mathematika (London) 47, 281-297 (2000).

L. Barker, Local representation theory and Mobius inversion, Comm. Alg. 27 (7), 3377-3399 (1999).

L. Barker, On the contractibility of the orbit space of a G-poset of Brauer pairs",J. Alg. 212, 460-465 (1999).

L. Barker, The dimension of a primitive interior G-algebra", Glasgow Math. J. 41, 151-155 (1999).

L. Barker, Counting positive defect irreducible characters of a finite group", New Zealand J. Math. 27, 167-176 (1998).

L. Barker, Alperin's fusion theorem and G-posets", J. Group Theory 1, 357-369 (1998).

L. Barker, Defects of irreducible characters of p-solvable groups", J. Alg. 202, 178-184 (1998).

L. Barker, The number of blocks with a given defect group", Mathematika (London) 44, 368-373 (1997).

L. Barker, On p-soluble groups and the number of simple modules associated with a given Brauer pair", Quart. J. Math. (Oxford) (Ser. 2) 48, 133-160 (1997).

L. Barker, Mobius inversion and the Lefschetz invariants of some p-subgroup complexes", Comm. Alg. 24 (8), 2755-2769 (1996).

L. Barker, G-algebras, Clifford theory, and the Green correspondence, J. Alg. 172, 335-353 (1995).

L. Barker, Modules with simple multiplicity modules, J. Alg. 172, 152-158 (1995).

L. Barker, Induction, restriction and G-algebras, Comm. Alg. 22 (15), 6349-6383 (1994).

L. Barker, Blocks of endomorphism algebras, J. Alg. 168, 728-740 (1994).


L. Barker, Tornehave morphisms III: the reduced Tornehave morphism and the Burnside unit functor, (submitted). tornehave3.pdf

Research students

Past students, PhD:

Ergun Yaraneri, 2008. Olcay Coskun, 2008. Ipek Tuvay, 2013.

Past students, MS:

Ayse Yaman, 2002. Ergun Yaraneri, 2003. Olcay Coskun, 2004. Mehmet Uc, 2008. Cihan Okay, 2009, Ipek Tuvay, 2009.
Daghan Yaylioglu, 2012. Yasemin Turedi, 2013. Merve Demirel, 2013.

Present students:

Hatice Mutlu, Ismail Alperen Ogut, Elif Dogan.


The files arch[...].pdf, below, are archives of course materials, including past papers.

Present courses:

(No 2014 summer semester courses.)

Past undergraduate courses:

MATH 103: Introductory Mathematics

MATH 110, Discrete Mathematics
Course archives: arch110fall13.pdfarch110fall12.pdf,

MATH 123 Abstract Mathematics I

MATH 124: Abstract Mathematics II

MATH 132: Discrete and Combinatorial Mathematics
Course archive: arch132spr14.pdf.

MATH 215, Mathematical Analysis
Course archive: arch215spr12.pdf
Notes on countability: count215spr12.pdf
Notes on construction of the reals: conreal215spr12.pdf

MATH 220: Linear Algebra
Note on diagonalization and change of basis: diagonalisation.pdf  

MATH 223: Linear Algebra I

MATH 224: Linear Algebra II
Course archive: arch224spr13.pdf.

MATH 313 Real Analysis II

MATH 323, Algebra I
Note on permutation groups: permutation.pdf
Note on determinants and the symmetric group: determinants.pdf

MATH 324, Algebra II

MATH 325 Representation Theory
Course archive: arch325spr13.pdf.

Past postgraduate courses:

MATH 500, Mathematical Analysis

MATH 523, Algebra I
Course archive: arch523fall12.pdf.

MATH 524, Algebra II

MATH 525 Group Representations
Course outline: intro525spr12.pdf

MATH 616: Topics in Group Theory

"An Introduction to Discrete Mathematics: how
to make mistakes, how to get it right"

The following two chapters of the book are in draft form.

Chapter 1, Mathematical Induction: discretehow1.pdf
Chapter 2, Recurrence Equations: discretehow2.pdf

PhD Qualifying Exam

This exam is part of the PhD Programme in Mathematics at Bilkent.

Exam outline and syllabus: qualsyl.pdf.

Past papers: qual14june.pdf,
qual08may.pdf qual08jan.pdfqual06nov.pdfqual06aug.pdf.


Accidents in Mathematics

An essay on Clifford theory for defect-zero blocks, How phases appear when reducing to quotient groups, for instance, as in Alperin's Conjecture, phasealp.pdf, 2013.

An essay on group functors, Group Functors in Plain English, group_plain.pdf, 2008.

Accidents in History and Philosophy

If material from the following PDF files were to be reproduced or adapted without acknowledgement, then I would object to the plagiarism.

A recreational introductory talk, Eudoxus: the origin of reasoning by creation and subtraction? creatsubtract.pdf, 2013.

A recreational colloquium paper, Why are Aristotle and Euclid so Modernistic? modern.pdf, 2007.

An appendix The duplication of the Square in Plato's Meno, commissioned for an ill-fated book proposal, menojul.pdf, 2006.

Prose Corner

"Today's liturgy was something to do with developments in finite group theoretics that had taken place about thirteen hundred years ago and that had caused their originator, Saunt Bly, to be Thrown Back by his Warden Regulant and to live out the remainder of his days on top of a butte surrounded by slines who worshipped him as a god. He even inspired them to stop consuming blithe, whereupon they became surly, killed him, and ate his liver out of a misconception that this was where he did his thinking." - Neal Stephenson, Anathem, page 21, Harper Collins, 2008.

Brief CV

1983-87: Mathematical Tripos, Cambridge, UK;.

1987-92, D.Phil. in Mathematics, Oxford University, UK.

1992-93, Postdoc at Ecole Normale Superieure, Paris, France.

1993, Postdoc at Universitat Augsburg, Germany.

1994-96: Postdoc at University of Wales, Cardiff, UK.

1996-date: Department of Mathematics, Bilkent University.

1997-98: Fellowship at Mathematisches Institut, Friedrich Schiller Universitat, Jena, Germany.

2010-11: Sabbatical at Department of Mathematics, University of California, Santa Cruz.


Addresses and numbers.

Postal Address: Bilkent University, Department of Mathematics, Bilkent, Ankara, 06800 Turkey.

Office: 129 Fen A. (In the crescent-shaped building overlooking the circular fountain.)

Phone: +90 312 290 2120.

Fax:  +90 312 290 5097.

Email: my surname, then the at sign, then fen rabbit bilkent rabbit edu rabbit tr, where rabbit  has to be replaced by a dot.

Latest update: 19 June 2014