James Parkinson

Mess Senior 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 Algebra research group and the Geometry, Topology, and Analysis research group. My research interests include Lie theory, combinatorial representation theory, random walk theory, and finite geometry. More specifically, I am currently interested in the combinatorics of buildings and generalised polygons, and 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

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups
(L. Gilch, S. Müller, J. Parkinson)
Math. Z. (to appear) (2016) (pdf)

Distance regularity in buildings and structure constants in Hecke algebras
(P. Abramenko, J. Parkinson, H. Van Maldeghem)
Preprint (2015) (pdf)

Limit theorems for random walks on Fuchsian buildings and Kac-Moody groups
(L. Gilch, S. Müller, J. Parkinson)
Preprint (2015) (pdf)

Buildings, groups of Lie type, and random walks
(J. Parkinson)
To appear in proceedings of "Groups, graphs, and random walks", Cortona, Italy, 2014 (2015) (pdf)

Regular sequences and random walks in affine buildings
(J. Parkinson, W. Woess)
Ann. Inst. Fourier 65 No. 2 (2015) 675-707. (pdf)

The combinatorics of automorphisms and opposition in generalised polygons
(J. Parkinson, B. Temmermans, H. Van Maldeghem)
Ann. Comb. 19 Issue 3 (2015) 567-619. (pdf)

On calibrated representations and the Plancherel Theorem for affine Hecke algebras
(J. Parkinson)
J. Algebraic Combin. 40 (2014) 331-371. (pdf)

A classification of commutative parabolic Hecke algebras
(P. Abramenko, J. Parkinson, H. Van Maldeghem)
J. Algebra 385 (2013) 115-133. (pdf)

Automorphisms and opposition in twin buildings
(A. Devillers, J. Parkinson, H. Van Maldeghem)
J. Austral. Math. Soc. 94 (2013) 189-201. (pdf)

A local limit theorem for random walks on the chambers of \tilde{A}_2 buildings
(J. Parkinson, B. Schapira)
Progr. Probab. 64, Birkhäuser, 15-53 (2011). (pdf)

Combinatorics in affine flag varieties
(J. Parkinson, A. Ram, C.Schwer)
J. Algebra 321 (2009) 3469-3493. (pdf)

Isotropic random walks on affine buildings
(J. Parkinson)
Ann. Inst. Fourier 57 (2007) 379-419. (pdf)

Spherical harmonic analysis on affine buildings
(J. Parkinson)
Math. Z. 253 (2006) 571-606. (pdf)

Buildings and Hecke algebras
(J. Parkinson)
J. Algebra 297 (2006) 1-49. (pdf)

Other

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


Undergraduate teaching

In Semester 1 2016, I am teaching:
MATH1901 Differential Calculus (Adv),
MATH3962 Rings fields and Galois Theory (Adv).

In Semester 2 2016, I am teaching:
MATH1014 Introduction to Linear Algebra, and a component of
MATH1907 on group theory.