Dr James Parkinson

F07 - Carslaw Building
The University of Sydney

Telephone 9351 4221
Fax 9351 4534

Website Personal web page

Research interests

I am a member of the Algebra research group and the Geometry, Topology, and Analysis research group. My research interests include combinatorial representation theory and random walk theory. More specifically, I am currently interested in the representation theory of Hecke algebras, with applications to probability theory on buildings and Kac-Moody groups. Other interests include generalised polygons, harmonic analysis on graphs and groups, and path models in Lie theory.

Teaching and supervision

Timetable

Selected grants

2011

  • The geometry and combinatorics of loop groups; Parkinson J, Kamnitzer J; Australian Research Council (ARC)/Discovery Projects (DP).

Selected publications

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Book Chapters

  • Parkinson, J., Schapira, B. (2011). A Local Limit Theorem for Random Walks on the Chambers of A2 Buildings. In Daniel Lenz, Florian Sobieczky, Wolfgang Woess (Eds.), Random Walks, Boundaries and Spectra, (pp. 15-53). Basel, Berlin: Springer.

Journals

  • Parkinson, J. (2014). On calibrated representations and the Plancherel Theorem for affine Hecke algebras. Journal of Algebraic Combinatorics, 40(2), 331-371. [More Information]
  • Abramenko, P., Parkinson, J., Van Maldeghem, H. (2013). A classification of commutative parabolic Hecke algebras. Journal of Algebra, 385, 115-133. [More Information]
  • Devillers, A., Parkinson, J., Van Maldeghem, H. (2013). Automorphisms and opposition in twin buildings. Journal of the Australian Mathematical Society, 94(2), 189-201. [More Information]
  • Parkinson, J., Ram, A., Schwer, C. (2009). Combinatorics in affine flag varieties. Journal of Algebra, 321(11), 3469-3493. [More Information]
  • Parkinson, J. (2007). Isotropic random walks on affine buildings. Annales de l'Institut Fourier, 57(2), 379-419.
  • Parkinson, J. (2006). Buildings and Hecke algebras. Journal of Algebra, 297(1), 1-49. [More Information]
  • Parkinson, J. (2006). Spherical harmonic analysis on affine buildings. Mathematische Zeitschrift, 253(3), 571-606. [More Information]

2014

  • Parkinson, J. (2014). On calibrated representations and the Plancherel Theorem for affine Hecke algebras. Journal of Algebraic Combinatorics, 40(2), 331-371. [More Information]

2013

  • Abramenko, P., Parkinson, J., Van Maldeghem, H. (2013). A classification of commutative parabolic Hecke algebras. Journal of Algebra, 385, 115-133. [More Information]
  • Devillers, A., Parkinson, J., Van Maldeghem, H. (2013). Automorphisms and opposition in twin buildings. Journal of the Australian Mathematical Society, 94(2), 189-201. [More Information]

2011

  • Parkinson, J., Schapira, B. (2011). A Local Limit Theorem for Random Walks on the Chambers of A2 Buildings. In Daniel Lenz, Florian Sobieczky, Wolfgang Woess (Eds.), Random Walks, Boundaries and Spectra, (pp. 15-53). Basel, Berlin: Springer.

2009

  • Parkinson, J., Ram, A., Schwer, C. (2009). Combinatorics in affine flag varieties. Journal of Algebra, 321(11), 3469-3493. [More Information]

2007

  • Parkinson, J. (2007). Isotropic random walks on affine buildings. Annales de l'Institut Fourier, 57(2), 379-419.

2006

  • Parkinson, J. (2006). Buildings and Hecke algebras. Journal of Algebra, 297(1), 1-49. [More Information]
  • Parkinson, J. (2006). Spherical harmonic analysis on affine buildings. Mathematische Zeitschrift, 253(3), 571-606. [More Information]

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