Staff profile

Qualifications

• MSc(Mon), PhD.(Manit) FAustMS.

Teaching areas

• Calculus and Number Systems at first-year (MAT1CNS).

• Applied Algebra at second-year (MAT2AAL).

• Group Theory and Lattice Theory at third-year (MAT3DS).

• General Algebra (= Universal Algebra) at honours level (MAT4GA).

Supervision

• Present PhD supervisions:

  Belinda Trotta “Axiomatisability of classes of Boolean topological graphs” (co-supervised with M. Jackson).
  Sarah Johansen “Dualisability of finite relational structures and partial algebras” (co-supervised with J. Pitkethly).
  Nadia Dhamri “Dualisability of finite semigroups” (co-supervised with M. Jackson).
  Thanh Long Nguyen “Priestley spaces” (co-supervised with J. Pitkethly).

• Recent PhD completions:

  Todd Niven “Variations on the full versus strong problem in the theory of natural dualities”, graduated 2006.

• Recent Honours Students
  2006 Sarah Johansen “Natural dualities for structures”.
  2004 Olivia Lo Schiavo “Finite basis theorems”.

Professional involvement

• I am an executive editor for Algebra Universalis and associate editor for the Bulletin of the Australian Mathematical Society.

• I am president of the Victorian Algebra Group and have been involved in it since it inception. The group organises the annual Victorian Algebra Conference, which is now in its 26th year.

Research interests

• My research interests centre on general (= universal) algebra and lattice theory. I am interested in the topological representation of algebras, with an emphasis on natural duality theory, and I am particularly interested in applications of duality theory to algebras with an underlying distributive lattice structure. See the web site of my research group for more details: Research Group on General Algebra and its Applications.

Recent publications and presentations

• J. Pitkethly and B. Davey, Dualisability: Unary Algebras and Beyond, Springer, 2005.
• 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., to appear.
• 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. 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.