James Parkinson

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

Address: A/Prof 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 buildings, Coxeter groups, Hecke algebras, Kazhdan-Lusztig theory, Lie theory, combinatorial representation theory, random walk theory, and incidence geometry. Other interests include harmonic analysis on graphs and groups, symmetric functions, Macdonald polynomials, and path models in Lie theory.

Here is my CV.

I am an editor for the following journals; see the links for the submission process.
Bulletin of the Australian Mathematical Society
Innovations in Incidence Geometry: Algebraic, Topological, and Combinatorial

Papers and preprints

Automorphisms and opposition in spherical buildings of exceptional type, V: The \({E}_8\) case
(J. Parkinson, H. Van Maldeghem)
Preprint, (2025) (pdf)

The asymptotic Plancherel formula and Lusztig's asymptotic algebra for \(\tilde{A}_n\)
(N. Chapelier-Laget, J. Guilhot, E. Little, J. Parkinson)
Preprint, (2024) (pdf)

Uniclass automorphisms of spherical buildings
(Y. Neyt, J. Parkinson, H. Van Maldeghem)
To appear in Geometriae Dedicata, (2025) (pdf)

Automorphisms and opposition in spherical buildings of exceptional type, IV: The \({E}_7\) case
(Y. Neyt, J. Parkinson, H. Van Maldeghem, M. Victoor)
Preprint, (2024) (pdf)

Automorphisms and opposition in spherical buildings of classical type
(J. Parkinson, H. Van Maldeghem)
Advances in Geometry, 24 (2024) 287-321(pdf)

On \(J\)-folded alcove paths and combinatorial representations of affine Hecke algebras
(J. Guilhot, E. Little, J. Parkinson)
Algebras and Representation Theory 27 (2024) 2131-2185 (pdf)

Automorphisms and opposition in spherical buildings of exceptional type, II: Moufang hexagons
(J. Parkinson, H. Van Maldeghem)
Innovations in Incidence Geometry, 20 (2023) 443-470 (pdf)

Cone types, automata, and regular partitions in Coxeter groups
(J. Parkinson, Y. Yau)
Advances in Mathematics, 398 (2022) (pdf)

Automorphisms and opposition in spherical buildings of exceptional type, I
(J. Parkinson, H. Van Maldeghem)
Canadian Journal of Mathematics, 74 (2022) 1517-1578 (pdf)

Patterns in sets of positive density in trees and affine buildings
(M. Björklund, A. Fish, J. Parkinson)
Groups, Geometry and Dynamics, 15 (2021) 1267-1295 (pdf)

Coxeter systems for which the Brink-Howlett automaton is minimal
(J. Parkinson, Y. Yau)
Journal of Algebra, 527 (2019) 437-446 (pdf)

Opposition diagrams for automorphisms of small spherical buildings
(J. Parkinson, H. Van Maldeghem)
Innovations in Incidence Geometry, 17 (2019) 141-188 (pdf)
Some associated MAGMA code (including minimal faithful permutation representations of various exceptional type \(\mathbb{ATLAS}\) groups)

Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for \(\tilde{C}_2\)
(J. Guilhot, J. Parkinson)
Algebraic Combinatorics, 2 (2019) 969-1031 (pdf)

Opposition diagrams for automorphisms of large spherical buildings
(J. Parkinson, H. Van Maldeghem)
Journal of Combinatorial Theory, Series A 162 (2019) 118-166 (pdf)

A proof of Lusztig's conjectures for affine type \(G_2\) with arbitrary parameters
(J. Guilhot, J. Parkinson)
Proceedings of the London Mathematical Society, 118 (2019) 1188-1244 (pdf)

Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings
(U. Baumgartner, J. Parkinson, J. Ramagge)
Journal of Algebra 520 (2019) 460-478 (pdf)

Limit theorems for random walks on Fuchsian buildings and Kac-Moody groups
(L. Gilch, S. Müller, J. Parkinson)
Groups, Geometry, and Dynamics 12 (2018) 1069-1121 (pdf)

Buildings, groups of Lie type, and random walks
(J. Parkinson)
Groups, graphs, and random walks
London Mathematical Society Lecture Note Series, 436 (2017) 391-443. (pdf)

Asymptotic entropy of random walks on Fuchsian buildings and Kac-Moody groups
(L. Gilch, S. Müller, J. Parkinson)
Mathematische Zeitschrift 285 (2017) 707-738. (pdf)

Distance regularity in buildings and structure constants in Hecke algebras
(P. Abramenko, J. Parkinson, H. Van Maldeghem)
Journal of Algebra 481 (2017) 158-187. (pdf)

Regular sequences and random walks in affine buildings
(J. Parkinson, W. Woess)
Annales de l'Institut Fourier 65 No. 2 (2015) 675-707. (pdf)

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

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

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

Automorphisms and opposition in twin buildings
(A. Devillers, J. Parkinson, H. Van Maldeghem)
Journal of the Australian Mathematical Society 94 (2013) 189-201. (pdf)

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

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

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

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

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

Other

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