Homepage for Laurence Barker
Group representation theorist, Associate Professor in the Department of Mathematics at Bilkent University.
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, 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, I. Tuvay, Real representation spheres and the real monomial Burnside ring, (J. Alg. to appear). realrevised.pdf
L. Barker, Tornehave morphisms III: the reduced Tornehave morphism and the Burnside unit functor, (submitted). tornehave3.pdf
Past students:
Ayse Yaman, MS, 2002. Ergun Yaraneri, PhD 2008. Olcay Coskun, PhD 2008. Mehmet Uc, MS, 2008. Cihan Okay, MS, 2009.Present students:
Ipek Tuvey, Daghan Yaylioglu, Merve Demirel, Yasemin Turedi.
Present undergraduate courses:
MATH 323, Algebra I:
MATH 220, Linear Algebra:
Course coutline: lin11fall1.pdf
Note on determinants and permutations: determinants.pdf
Note on diagonalization and change of basis: diagonalisation.pdf
Midterm 1, questions, solutions and comments: exama22011.pdf
Midterm 2, questions, solutions and comments: examb22011.pdf
Past undergraduate courses:
MATH 103: Introductory Mathematics,
MATH 123 Abstract Mathematics I,
MATH 124: Abstract Mathematics II,
MATH 132: Discrete and Combinatorial Mathematics,
Handout 1: Course outline:
discrete1.pdf
Handout 2: Mathematical proof, especially proof by induction:
discrete2.pdf
Handout 3: Present exam papers, solutions, comments on mistakes:
collSpr09.110.pdf
Past papers: coll07.110.pdf,
coll08.110.pdf
MATH 220: Linear Algebra,
MATH 223: Linear Algebra I,
MATH 224: Linear Algebra II,
MATH 313 Real Analysis II,
MATH 323, Algebra I,
MATH 324, Algebra II,
MATH 325 Representation Theory.
Past postgraduate courses:
MATH 523, Algebra I,
MATH 524, Algebra II,
MATH 525 Group Representations,
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: qual09jan.pdf, qual08may.pdf, qual08jan.pdf, qual06nov.pdf, qual06aug.pdf.
Links.
If material from the following PDF files were to be reproduced or adapted without acknowledgement, then I would object to the plagiarism.
An essay on group functors, Group Functors in Plain English, group_plain.pdf. (Culturally accessible to those who can follow the gist of, say, the mathematical concepts in the film Resident Evil Apocalypse.)
A recreational colloquium paper, Why are Aristotle and Euclid so Modernistic? modern.pdf. (Accessible to those who can mathematically cope with the film Resident Evil Extinction.)
An appendix The duplication of the Square in Plato's Meno, commissioned for an ill-fated book proposal, menojul.pdf. (Accessible to those who can solve most of the mathematical problems that appear in the computer game Resident Evil Nemesis.)
"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 worshopped 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.
Latest update: 2 January 2012.