# James Parkinson

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 Room 614 Carslaw Building jamesp@maths.usyd.edu.au +61 2 9351 4221 +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, Lie theory, combinatorial representation theory, random walk theory, and incidence geometry. I am currently interested in the combinatorics of buildings and generalised polygons, the representation theory of Hecke algebras, Kazhdan-Lusztig theory, and 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 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

Opposition diagrams for automorphisms of small spherical buildings
(J. Parkinson, H. Van Maldeghem)
Submitted (2018) (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)
Submitted (2018) (pdf)

Opposition diagrams for automorphisms of large spherical buildings
(J. Parkinson, H. Van Maldeghem)
Submitted (2017) (pdf)

A proof of Lusztig's conjectures for affine type $$G_2$$ with arbitrary parameters
(J. Guilhot, J. Parkinson)
Submitted (2017) (pdf)

Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings
(U. Baumgartner, J. Parkinson, J. Ramagge)
Submitted (2017) (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)
Math. Z. 285 (2017) 707-738. (pdf)

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

Limit theorems for random walks on Fuchsian buildings and Kac-Moody groups
(L. Gilch, S. Müller, J. Parkinson)
Groups, Geometry, and Dynamics, to appear (2017) (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)