**Homepage for Laurence Barker**

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

I try to respond to e-mails properly, but not promptly.

All social media entities associated with me are dead or fake.

**Index:**

- Current research interests
- Publications
- Research students
- Lecture courses
- An Introduction to Discrete Mathematics
- PhD Qualifying Exam
- Notes and essays
- 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.

*An inversion formula for the primitive
idempotents of the trivial source algebra*.

Journal of Pure and Applied Algebra (to appear).
primitive.pdf, also
https://arxiv.org/abs/1809.10984

with Hatice Mutlu, *A new canonical induction formula for
p-permutation modules*.

Comptes Rendus Mathematique, 357, 327-332 (2019).
canonicalInduction.pdf, also
https://arxiv.org/abs/1811.02877

*A general approach to Green functors using bisets*,

Communications in Algebra 44 (12), 5351-5375 (2016).
generalgreenrev.pdf

with Merve Demirel, *Simple functors of admissible linear categories*,

Algebras and Representation Theory 19, 463-472 (2016).
admissibleRevised.pdf

with Ipek Tuvay, *A refinement of Alperin's conjecture for blocks of the
endomorphism algebra
of the Sylow permutation module*,

Archiv der Mathematik 106, 15-20 (2016). refinementAlperinFinal

*Blocks of Mackey categories*,

Journal of Algebra 446, 34-57 (2016).
blocksmackeyrev.pdf

*Tornehave morphisms III: the reduced Tornehave morphism and the
Burnside unit functor*,

Journal of Algebra 446, 19-33 (2016).
torne3rev.pdf

with Ipek Tuvay, *Real representation spheres and the real monomial
Burnside ring*,

J. Algebra 353, 79-92 (2012). realrevised.pdf

*Tornehave morphisms I: resurrecting the virtual permutation sets
annihilated by linearization*,

Communications in Algebra 39, 355-395 (2011).
tornehave1rev.pdf

*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

*Rhetorical biset functors, rational p-biset functors and their semisimplicity
in characteristic zero*,

J. Algebra 319, 3810-3853 (2008).
semisim_preprint.pdf

*Genotypes of irreducible representations of finite p-groups*,

J. Algebra, 306, 655-681 (2007).
genetic_preprint.pdf

*Fibred permutation sets and the idempotents and units of monomial Burnside rings*,

J. Algebra 281, 535-566 (2004).

with Ergun 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).

*Continuum quantum systems as limits of discrete quantum systems. IV.
Affine Canonical Transforms*,

J. Math. Phys. 44, 1535-1553 (2003).

*Continuum quantum systems as limits of discrete quantum systems. III. Operators*,

J. Math. Phys. 42 (10), 4652-4668 (2001) .

*Continuum quantum systems as limits of discrete quantum systems, II: state functions*,

J. Phys. A: Math. Gen. 22, 4673-4682 (2001).

*Continuum quantum systems as limits of discrete quantum systems. I: state vectors*,

J. Functional Analysis 186, 153-166 (2001).

with Cagatay Candan, Tugrul Hakioglu, M. Alper Kutay, Haldun Ozaktas,
*The discrete harmonic
oscillator, Harper's equation, and the discrete fractional Fourier transform*,

J. Phys. A: Math. Gen. 33, 2209-2222 (2000).

*The discrete fractional Fourier transform and Harper's equation*,

Mathematika (London) 47, 281-297 (2000).

*Local representation theory and Mobius inversion,*

Comm. Alg. 27 (7), 3377-3399 (1999).

*On the contractibility of the orbit space of a G-poset of Brauer pairs*,

J. Alg. 212, 460-465 (1999).

*The dimension of a primitive interior G-algebra*,

Glasgow Math. J. 41, 151-155 (1999).

*Counting positive defect irreducible characters of a finite group*,

New Zealand J. Math. 27, 167-176 (1998).

*Alperin's fusion theorem and G-posets*,

J. Group Theory 1, 357-369 (1998).

*Defects of irreducible characters of p-solvable groups*,

J. Alg. 202, 178-184 (1998).

*The number of blocks with a given defect group*,

Mathematika (London) 44, 368-373 (1997).

*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).

*Mobius inversion and the Lefschetz invariants of some p-subgroup complexes*,

Comm. Alg. 24 (8), 2755-2769 (1996).

*G-algebras, Clifford theory, and the Green correspondence*,

J. Alg. 172, 335-353 (1995).

*Modules with simple multiplicity modules*,

J. Alg. 172, 152-158 (1995).

*Induction, restriction and G-algebras*,

Comm. Alg. 22 (15), 6349-6383 (1994).

*Blocks of endomorphism algebras*,

J. Alg. 168, 728-740 (1994).

**Past students, PhD:**

**Past students, MS:**

Daghan Yaylioglu, 2012. Yasemin Turedi, 2013. Merve Demirel, 2013. Ismail Alperen Ogut, 2014. Elif Dogan, 2015. Cisil Karaguzel, 2016. Andi Nika, 2018.

**Present students:**

Course specification: spec104spr19.pdf.

Midterm 1 with solutions: mida104spr19.pdf.

Midterm 2 with solutions: midb104spr19.pdf.

Final with solutions: fin104spr19.pdf.

Course specification: spec227spr19.pdf.

Suggested exercises and quizzes: exerquiz227spr19.pdf.

Source material for Midterm 1 revision: midterm1revision227spr19.pdf.

Midterm 1 with solutions: mida227spr19.pdf.

Midterm 2 with solutions: midb227spr19.pdf.

Midterm 2 Makeup: midbmak227spr19.pdf.

Final with solutions: fin227spr19.pdf.

Some notes on diagonalization: diagonalisation.pdf.

Archives of past course materials, including quizzes, exams and

solutions: arch227fall18.pdf, arch227spr17.pdf.

Course archives: arch110fall14.pdf, arch110fall13.pdf, arch110fall12.pdf,

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

Course archive: arch123fall17.pdf.

Course archives: arch132fall15.pdf, arch132spr14.pdf, arch132fall17.pdf.

Course archives: arch210spr16.pdf, arch210spr15.pdf.

Course archive: arch215spr12.pdf.

Notes on countability: count215spr12.pdf

Notes on construction of the reals: conreal215spr12.pdf

Course archive: arch220fall11.pdf.

Course archive: arch224spr13.pdf.

Course archives: arch227fall18.pdf, arch227spr17.pdf.

Course archives: arch323fall16.pdf, arch323fall14.pdf.

Course archives: arch325spr18.pdf, arch325spr13.pdf.

**Past postgraduate courses:**

**MATH 523: Algebra I**

Course archives: arch523fall16.pdf,
arch523fall12.pdf.

**MATH 524: Algebra II**

Course archive: arch524spr15.pdf.

**MATH 525: Group Representations**

Course archives: arch525spr18.pdf,
arch525spr12.pdf.

**MATH 527: Topics in Representation Theory**

Course archive: arch527spr16.pdf.

**MATH 616: Topics in Group Theory**

Chapter 1, Very clear deductive explanation.

Chapter 2, Graph theory. dincom2.pdf

Chapter 3, Mathematical induction and the Euclidian algorithm.

Chapter 4, Enumerative combinatorics and binomial coefficients. dincom4.pdf

Chapter 5, Correspondences and functions.

Chapter 6, Relations, equivalence relations, posets.

Chapter 7, Isomorphism.

The courses MATH 110, 132, 210 all have similar

material. Some past exam papers and solutions are

collected in discretepastpapers.pdf.

For a larger collection, see the course archives, above, for MATH 110, 132, 210.

Some very incomplete

Note on

Note on

Note on

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

Exam outline and syllabus: qualsyl.pdf.

Past papers: qual18oct.pdf,

qual16june.pdf,
qual16jan.pdf,
qual15july.pdf,
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.

Reproduction or adaptation without acknowledgement is plagiarism.

Lecture course on "Functorial Methods in Representation Theory",

Summer School, 7-18 August 2017 Nesin Mathematics Village, Serince.

*Block Fusion Systems *
BlockFusionSystems.pdf, 2017.

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.

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 is to be replaced by a dot.

Latest update: 10 June 2019