James Parkinson

Mess Lecturer in the School of Mathematics and Statistics at the University of Sydney.

Address: Dr James Parkinson
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 614 Carslaw Building
Email: jamesp@maths.usyd.edu.au
Phone: +61 2 9351 4221
FAX: +61 2 9351 4534

Research Interests

I am a member of the Analysis research group and the Algebra 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 harmonic analysis on graphs and groups, symmetric functions, Macdonald polynomials, and path models in Lie theory. Here is my Curriculum Vitae.

Papers and Preprints

Automorphisms and opposition in twin buildings (joint with A. Devillers and H. Van Maldeghem), Preprint (2012) (pdf)

A classification of commutative parabolic Hecke algebras (joint with P. Abramenko and H. Van Maldeghem), Preprint (2011) (pdf)

On calibrated representations and the Plancherel Theorem for affine Hecke algebras, Preprint (2011) (pdf)

A local limit theorem for random walks on the chambers of \tilde{A}_2 buildings (joint with B. Schapira), Progress in Probability, Vol.64, Birkhäuser, 15-53 (2011). (pdf)

Combinatorics in affine flag varieties, (with A. Ram and C.Schwer), Journal of Algebra 321 (2009) 3469-3493. (pdf)

Alcove walks, buildings, symmetric functions and representations (joint with A. Ram), Preprint (2008) (pdf)

Isotropic random walks on affine buildings, Annales de L'Institut Fourier 57 (2007) 379-419. (pdf)

Spherical harmonic analysis on affine buildings, Mathematische Zeitschrift 253 (2006) 571-606. (pdf)

Buildings and Hecke algebras, Journal of Algebra 297 (2006) 1-49. (pdf)

Buildings and Hecke algebras, PhD Thesis University of Sydney (2005). (pdf)

Undergraduate teaching

In first semester 2011 I will be teaching MATH2961 and Functional Analysis.

In second semester 2011 I will be teaching MATH1903 and MATH1014

Honours and postgraduate teaching

I am happy to supervise students (reading courses, honours projects, or postgraduate degrees) on a range of topics including combinatorial representation theory, probability theory (random walks) and harmonic analysis on graphs and groups. Here is a list of potential topics.

Administrative matters

I am currently the second year pure mathematics coordinator. Queries related to such matters should be addressed to pm2coord@maths.usyd.edu.au.