Professor Brian A.

Professor Brian A. Davey

FAustMS

Emeritus Professor

College of Science, Health and Engineering

School of Engineering and Mathematical Sciences

Department of Mathematics and Statistics

Physical Sciences 2, Room 216, Melbourne (Bundoora)

Qualifications

BSc (Hon.), MSc Monash. PhD Manit.

Role

Academic

Membership of professional associations

Fellow of the Australian Mathematical Society

Area of study

Mathematics and Statistics

Brief profile

Prof. Davey's research interests centre on general (= universal) algebra and lattice theory. He is interested in the topological representation of algebras, with an emphasis on natural duality theory, and is particularly interested in applications of duality theory in general and Priestley duality in particular to algebras with an underlying distributive lattice structure. See the web site of his research group for more details: Research Group on General Algebra and its Applications.

Prof. Davey's journal articles are available to download from ResearchGate.

A full CV is available here, or at the bottom of this page.

For information about Prof. Davey's non-mathematical interests, please see his personal website.

Research interests

General algebra

- Natural dualities and applications of Priestley duality

Teaching units

Subjects taught recently:

  • MAT1CNS Calculus and Number Systems (at first-year).
  • MAT2AAL Applied Algebra (at second-year).
  • MAT3DS Group Theory and Lattice Theory (at third-year).
  • MAT4GA General Algebra (= Universal Algebra) (at honours level).
  • MAT4DT Duality Theory (at honours level).

 

Recent publications

  Prof. Davey's journal articles are available to download from ResearchGate.

Books

Book Chapters

  • B. A. Davey, Terrance Speed—Commentary on Selected Algebra Papers, Selected Works of Terry Speed (S. Dudoit, ed.), Springer, 2011, pp. 1–5.
  • B. A. Davey and M. Haviar, Modified Priestley dualities as natural dualities, Lattice Theory: Foundation (G. Grätzer), Springer, 2011, pp. 434–437.
  • B. A. Davey and H. A. Priestley, Distributive lattices and duality, General Lattice Theory (G. Grätzer), Second edition, Birkhäuser, 1998, pp. 499–517.
  • B. A. Davey and I. G. Rosenberg, Natural dualities and clones, Advances in Mathematical Sciences: CRM's 25 Years (Montreal, 1994) (L. Vinet, ed.), CRM Proc. Lecture Notes 11, Amer. Math. Soc., 1997, pp. 385–402.
  • B. A. Davey, Dualisability in general and endodualisability in particular, Logic and Algebra (Pontignano, 1994) (A. Ursini and P. Aglianò, eds), Lecture Notes in Pure and Appl. Math. 180, Dekker, 1996, pp. 437–455.
  • B. A. Davey and R. W. Quackenbush, Bookkeeping duality for paraprimal algebras, Contributions to General Algebra 9 (Linz, 1994) (H. K. Kaiser et al., eds), Hölder-Pichler-Tempsky, 1995, pp. 19–26.
  • B. A. Davey, Duality theory on ten dollars a day, Algebras and Orders (Montreal, 1991) (I. G. Rosenberg and G. Sabidussi, eds), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 389, Kluwer, 1993, pp. 71–111.
  • B. A. Davey and H. Werner, Piggyback dualities, Lectures in Universal Algebra (Szeged, 1983) (L. Szabó and Á. Szendrei, eds), Colloq. Math. Soc. János Bolyai 43, North-Holland, 1986, pp. 61–83.
  • B. A. Davey and H. Werner, Dualities and equivalences for varieties of algebras, Contributions to Lattice Theory (Szeged, 1980) (A. P. Huhn and E. T. Schmidt, eds), Colloq. Math. Soc. János Bolyai 33, North-Holland, 1983, pp. 101–275.
  • B. A. Davey and D. Duffus, Exponentiation and duality, Ordered Sets (Banff, 1981) (I. Rival, ed.), NATO Adv. Study Inst. Ser. C: Math. Phys. Sci. 83, Reidel, 1982, pp. 43–95.
  • B. A. Davey, Topological duality for prevarieties of universal algebras, Studies in Foundations and Combinatorics (G.-C. Rota, ed.), Adv. in Math. Suppl. Stud. 1, Academic Press, 1978, pp. 61–99.

Journal Articles: Mathematics

  • B. A. Davey, The product representation theorem for interlaced pre-bilattices: some historical remarks, Algebra Universalis, to appear. 
  • B. A. Davey, W. Bentz, J. G. Pitkethly and R. Willard, Dualizability of automatic algebras, J. Pure Appl. Algebra, to appear.
  • B. A. Davey, J. G. Pitkethly and R. Willard, The lattice of alter egos (PDF 397KB), Internat. J. Algebra Comput.,  22 (2012), 1250007, 36 pp. 
  • B. A. Davey, M. Haviar and H. A. Priestley, Natural dualities in partnership, Appl. Categ. Structures,  20 (2012), 583–602.
  • B. A. Davey and H. A. Priestley, Canonical extensions and discrete dualities for finitely generated varieties of lattice-based algebras, Studia Logica 100 (2012), 137-161.
  • B. A. Davey, M. Haviar and J. G. Pitkethly, Full dualisability is independent of the generating algebra, Algebra Universalis 67 (2012),  257–272.
  • B. A. Davey and H. A. Priestley, A topological approach to canonical extensions in finitely generated varieties of lattice-based algebras, Topology and its applications 158 (2011), 1724–1731.
  • B. A. Davey, M. J. Gouveia, M. Haviar and H. A. Priestley, Natural extensions and profinite completions of algebras, Algebra Universalis, 66 (2011), 331–336.
  • B. A. Davey, M. Jackson, J. G. Pitkethly and Cs. Szabó, Finite degree: algebras in general and semigroups in particular, Semigroup Forum, 83 (2011), 89–110.
  • B. A. Davey, M. J. Gouveia, M. Haviar and H. A. Priestley, Multisorted dualisability: change of base, Algebra Universalis, 66 (2011), 331–336.
  • B. A. Davey, M. Haviar and J. G. Pitkethly, Using coloured ordered sets to study finite-level full dualities,Algebra Universalis 64 (2010), 69–100.
  • B. A. Davey and J. G. Pitkethly, Counting the relations compatible with an algebra, Internat. J. Algebra Comput. 20 (2010), 901–922.
  • D. M. Clark, B. A. Davey, J. G. Pitkethly and D. L. Rifqui, Flat unars: the primal, the semi-primal and the dualisable, Algebra Universalis 63 (2010), 303–329.
  • B. A. Davey, M. Jackson, M. Maróti and R. N. McKenzie, Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties, J. Aust. Math. Soc. 85 (2008), 59–74.
  • D. M. Clark, B. A. Davey, M. Jackson and J. G. Pitkethly, The axiomatizability of topological prevarieties, Adv. Math. 218 (2008), 1604–1653.
  • B. A. Davey, M. Jackson, J. G. Pitkethly and M. R. Talukder, Natural dualities for semilattice-based algebras, Algebra Universalis 57 (2007), 463–490.
  • D. M. Clark, B. A. Davey and R. Willard, Not every full duality is strong! (PDF 114KB), Algebra Universalis 57(2007), 375–381.
  • B. A. Davey, M. Haviar and H. A. Priestley, Boolean topological distributive lattices and canonical extensions, Appl. Categ. Structures 15 (2007), 225–241.
  • B. A. Davey, J. G. Pitkethly and R. Willard, Dualisability versus residual character: a theorem and a counterexample, J. Pure Appl. Algebra 210 (2007), 423–435.

 

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