**Homepage for Laurence Barker**

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

**Index:**

- Current research interests
- Publications
- Preprints
- Research students
- Lecture courses, handouts, past-papers
- An Introduction to Discrete Mathematics
- PhD Qualifying Exam
- Links
- Accidents in History and Philosophy
- Prose
- Brief CV
- Addresses and numbers

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

**Past students, PhD:**

**Past students, MS:**

Daghan Yaylioglu, 2012. Yasemin Turedi, 2013. Merve Demirel, 2013.

**Present students:**

Course outline: intro210spr15.pdf.

Homeworks and quizzes: hw210spr15.pdf.

This course is similar in syllabus to MATH 110 and 132. For past exam papers, see discretepastpapers.pdf. For further material, see the course archives, below, for MATH 110 and 132. Also see two chapters, below, of the book "An Introduction to Discrete Mathematics".

Course outline: intro524spr15.pdf.

Homeworks: hw524spr15.pdf.

Course archives: arch110fall14.pdf, arch110fall13.pdf,

arch110fall12.pdf, arch110spr09.pdf, arch110spr08.pdf, arch110spr07.pdf.

Course archive: arch132spr14.pdf.

Course archive: arch215spr12.pdf

Notes on countability: count215spr12.pdf

Notes on construction of the reals: conreal215spr12.pdf

Note on diagonalization and change of basis: diagonalisation.pdf

Course archive: arch224spr13.pdf.

Course archive: arch323fall14.pdf.

Note on permutation groups: permutation.pdf

Note on determinants and the symmetric group: determinants.pdf

Course archive: arch325spr13.pdf.

**Past postgraduate courses:**

**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**

to make mistakes, how to get it right"

Chapter 1, Mathematical Induction: discretehow1.pdf

Chapter 2, Recurrence Equations: discretehow2.pdf

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

Exam outline and syllabus: qualsyl.pdf.

Past papers: qual14june.pdf,

qual14jan.pdf,
qual13sept.pdf,
qual12july.pdf,
qual11sept.pdf,

qual10june.pdf,
qual10jan.pdf,
qual09june.pdf,
qual09jan.pdf,

qual08may.pdf,
qual08jan.pdf,
qual06nov.pdf,
qual06aug.pdf.

**Links**.

- 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

Reproduction or adaptation without acknowledgement is plagiarism.

Some mathematics useful for understanding Plato, *What a group is,
according to Plato
*, groupplato.pdf, 2014.

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.

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: 18th February 2015