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Last update: 26 November 2007
Dr David Pask
Operator Algebra: My primary interest is in a field of Pure Mathematics called Operator Algebra. Operator algebras we first formulated in the 1930s as Mathematicians began to formalise quantum mechanics. Since then operator algebras have played a role in many areas of Mathematics and theoretical Physics. Specifically, I am interested in the operator algebras generated by operators which satisfy relations encoded by a directed graph. My work has shown that many properties of the operator algebra can be read off from properties of the directed graph. There are also interesting connections with combinatorial topology and nonabelian duality. Lately, I have been working on higher dimensional versions of directed graphs, called k-graphs, which contain much more information and provide the potential for new applications.
Dynamical Systems: I have a secondary, but nonetheless important interest in an area of Dynamical Systems called Symbolic Dynamics. Symbolic dynamical systems provide models for many dynamical systems and have applications in Statistics, Computing and Coding theory. From my point of view, symbolic dynamical systems are interesting as they may be modeled by the paths in a directed graph and so have an important connection with my work in Operator Algebra. My work has shown that there are strong connections between the dynamical properties of the systems modeled by a directed graph and the algebraic properties of the operator algebra associated to the directed graph. Lately, I have been interested in dynamical systems modeled by a labeled directed graph, such systems are much more complicated as one can give many different edges in a graph the same label.
· 20062008: Chief Investigator on ARC Discovery Project: Pictures for Operator Algebras: higher-rank graphs; held jointly with Dr Aidan Sims, funded at A$279,000.
· 2004: NSF-CBMS Regional Conference in the Mathematical Sciences: Graph algebras: Operator Algebras We Can See; held jointly with Prof. P. Muhly and Dr M. Tomforde, funded at A$41,000. Conference held at University of Iowa, May 2004.
· 20012005: Various small grants from University of Newcastle, funding totaling A$31,000.
Papers and Preprints
Here is a list of my publications and preprints. If you are interested in a copy, just click the title to link to the journal article online, or the [PDF] hyperlink for a preprint version. If you dont currently have a PDF viewer, Adobe Reader supports both MacOSX and Windows, and can be downloaded for free from Adobes website.
· D.A. Pask. Ergodicity of certain cylinder flows, University of Warwick, 1990. [PDF]
Refereed Journal Publications:
· D. Pask, I. Raeburn, M. Rψrdam and A. Sims. Rank-two graphs whose C*-algebras are direct limits of circle algebras. J. Funct. Anal. 239 (2006), 137178. [PDF]
· D. Pask and A. Rennie. The Noncommutative Geometry of Graph C*-algebras I: The Index Theorem. J. Funct. Anal. 233 (2006), 92134. [PDF]
· S. Allen, D. Pask and A. Sims. A dual graph construction for higher rank graphs, and K-theory for finite 2-graphs. Proc. Amer. Math. Soc. 134 (2006), 455464. [PDF]
· K. Deicke, D. Pask and I. Raeburn. Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces. Internat. J. Math. 14 (2003), 773789. [PDF]
· D. Pask, I. Raeburn and T. Yeend. Actions of semigroups on directed graphs and their C*-algebras. J. Pure Appl. Algebra 159 (2001), 297313. [PDF]
· D. Pask and I. Raeburn. Symmetric Imprimitivity Theorems for Graph C*-algebras. Internat. J. Math. 12 (2001), 609623. [PDF]
· D. Pask and I. Raeburn. On the K-theory of Cuntz-Krieger algebras. Publ. Res. Inst. Math. Sci. 32 (1996), 415443. [PDF]
· D.A. Pask and C.E. Sutherland. Filtered inclusions of path algebras; a combinatorial approach to Doplicher-Roberts duality. J. Operator Theory 31 (1994), 99121. [PDF]
· D.A. Pask. Ergodicity of certain cylinder flows. Israel J. Math. 76 (1991), 129152. [PDF]
· D.A. Pask. Skew products over the irrational rotation. Israel J. Math. 69 (1990), 6574. [PDF]
Refereed Conference Publications:
· D. Pask and S-J. Rho. Some intrinsic properties of simple graph C*-algebras, Proceedings of the conference on Operator Algebras and Mathematical Physics, Constanta, 2001, 325340, (editors J-M. Combes, J. Cuntz, G.A. Elliot, G. Nenciu, H. Siedentop and S. Stratilia). Theta, Bucharest (2003). [PDF]
· D. Pask. Cuntz-Krieger algebras associated to directed graphs, Operator algebras and quantum field theory, Rome, 1996, 8592, (editors S. Doplicher, R. Longo, J.E. Roberts and L. Zsido). Int. Press, Cambridge, MA (1997). [PDF]