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:
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, A general approach to Green functors using bisets, Communications in Algebra 44 (12), 5351-5375 (2016). generalgreenrev.pdf
L. Barker, M. Demirel, Simple functors of admissible linear categories, Algebras and Representation Theory 19, 463-472 (2016). admissibleRevised.pdf
L. Barker, I. 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
L. Barker, Blocks of Mackey categories, Journal of Algebra 446, 34-57 (2016). blocksmackeyrev.pdf
L. Barker, Tornehave morphisms III: the reduced Tornehave morphism and the Burnside unit functor, Journal of Algebra 446, 19-33 (2016). torne3rev.pdf
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).
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.Present students:
Hatice Mutlu, Ismail Alperen Ogut, Andi Nika.Past postgraduate courses:
MATH 500: Mathematical AnalysisMATH 523: Algebra I
Course archives: arch523fall16.pdf,
arch523fall12.pdf.
MATH 524: Algebra II
Course archive: arch524spr15.pdf.
MATH 525: Group Representations
Course outline: intro525spr12.pdf.
MATH 527: Topics in Representation Theory
Course archive: arch527spr16.pdf.
MATH 616: Topics in Group Theory
This exam is part of the PhD Programme in Mathematics at Bilkent.
Exam outline and syllabus: qualsyl.pdf.
Past papers: 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.
Latest update: 18 April 2018