Geometry, algebra and combinatorics and their applications,
including the theory of error-correcting codes and cryptology.
Other academic interests:
Theoretical computer science and mathematical physics.
I am an Associate Professor in pure mathematics in the Department of Mathematics and Statistics at UWA.
Gordon Royle , of the Department of Computer Science, and I together direct the Combinatorial Computing Research Group at UWA.
I often collaborate with members of the Institute for Geometry and its Applications at the University of Adelaide,
especially Christine O'Keefe , who's now moved on to CSIRO in Canberra.
Challenge Problem Here is a 357 x 357 matrix of zeroes and ones. The eigenvalues of this matrix are 256,4 and -16. The algebraic and geometric multiplicity of the eigenvalue -16 is 84. Is there an eigenvector corresponding to the eigenvalue -16 with only the two values -6 and 11 for its components, with 11 occurring 126 times? In other words, is a permutation of the vector (11^126,-6^231) an eigenvector corresponding to the eigenvalue -16? If you can solve this problem, either positively by finding such an eigenvector, or negatively, by proving there is no such eigenvector, please email me.
Shane Kelly, honours student, jointly supervised with Michael Giudici, working on topics in classical groups and polar spaces, especially m-ovoids in unitary spaces.
I am always looking for honours and postgraduate students. Of my former students listed below, Rebecca Gower, Katrina Hicks and Nick Gill completed doctorates in Queensland, Oxford and Cambridge, and Nicholas Hamilton, Ivano Pinneri, Tim Boykett, Blair Williams and Maska Law had postdoctoral positions in Gent(Belgium), Rome(Italy), Linz(Austria), London(England) and Rome(Italy), respectively. My former student, Nicholas Hamilton, won the Kirkman medal of the Institute of Combinatorics and its Applications as did my research associate, Matthew Brown.
John Bamberg (jointly supervised with Cheryl Praeger) Thesis : Innately transitive groups (2003)
Maska Law Thesis : Flocks, generalised quadrangles and translation planes from BLT-sets (2003)
Blair Williams Thesis : Ovoids of hyperbolic and parabolic spaces (1998)
Tim Boykett (jointly supervised with Gunter Pilz) Thesis : Algebraic aspects of reversible computation (1996)
Ivano Pinneri Thesis : Flocks, generalised quadrangles and hyperovals (1996)
Nicholas Hamilton Thesis : Maximal arcs in finite projective planes and associated structures in projective spaces (1995)
Ranga Muhandiramge (jointly supervised with Jingbo Wang)
Thesis : Spin Adapted Configuration Interaction Study of N-electron Quantum Dots (2003)
Danijela Cvoro Thesis : Poincare's theorem for compact polygons(2000)
Nick Gill Thesis : Galois theory and orthogonal geometry(1998)
Maska Law Thesis : The Klein correspondence (1997)
Kenneth Phillips Thesis : Ovals, conics and Segre's theorem(1997)
Nicholas Hamilton Thesis : Group representation theory and applications to quantum mechanics (1991)
Ivano Pinneri Thesis : Propositional calculus of quantum mechanics (1990)
Katrina Hicks (jointly supervised with Michael Alder) Thesis : Automata (1990)
Rebecca Gower Thesis : Finite Generalized Quadrangles (1989)
Michel Lavrauw, Eindhoven, Netherlands (2001)
Elisabeth Kuijken, Gent, Belgium (2002)
Rocco Trombetti, Napoli, Italy (2002)
John Bamberg Australian Research Council Australian Postdoctoral Fellow (2004-6)
Matthew Brown Australian Research Council Senior Research Associate (2003-5)
Australian Research Council Research Associate (1998-9)(Adelaide)
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Author : Tim Penttila