Research
Preprints:
KK-duality for self-similar groupoid actions on graphs
With Nathan Brownlowe, Alcides Buss, Daniel Gonçalves, Jeremy B. Hume, and Aidan SimsA geometric representative for the fundamental class in KK-duality of Smale spaces
With Dimitris Gerontogiannis and Joachim ZachariasSelf-similarity and limit spaces of substitution tiling semigroups
With Jamie WaltonC*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
With Zahra Afsar, Nathan Brownlowe and Jacqui Ramagge
In print:
An aperiodic tile with edge-to-edge orientational matching rules
With Jamie Walton
Journal of the Institute of Mathematics of Jussieu, first view (2021), 1-27.An aperiodic monotile that forces nonperiodicity through dendrites
With Michael Mampusti
Bulletin of the London Mathematical Society, 52 (2020), 942-959.The Cuntz--Toeplitz algebras have nuclear dimension one
With Philip Easo, Esperanza Garijo, Sarunas Kaubrys, David Nkansah, Martin Vrabec, David Watt, Cameron Wilson, Christian Bönicke, Samuel Evington, Marzieh Forough, Sergio Girón Pacheco, Nick Seaton, Stuart White, Joachim Zacharias
Journal of Functional Analysis, 279 (2020), 1-14.Wieler solenoids, Cuntz-Pimsner algebras and K-theory
With Robin Deeley , Magnus Goffeng and Bram Mesland
Ergodic Theory and Dynamical Systems, 38 (2018), 2942-2988.Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs
With Marcelo Laca, Iain Raeburn and Jacqui Ramagge
Advances in Mathematics, 331 (2018), 268-325.K-theoretic duality for hyperbolic dynamical systems
With Jerry Kaminker and Ian F. Putnam
Journal für die Reine und Angewandte Mathematik (Crelle's Journal), 730 (2017), 263-299.Zappa-Szép product groupoids and C*-blends
With Nathan Brownlowe, David Pask, Jacqui Ramagge and Dave Robertson
Semigroup Forum, 94 (2017), 500-519.Graph algebras and orbit equivalence
With Nathan Brownlowe and Toke Meier Carlsen
Ergodic Theory and Dynamical Systems, 37 (2017), 389-417.Fractal spectral triples on Kellendonk's C*-algebra of a substitution tiling
With Michael Mampusti
Journal of Geometry and Physics, 112 (2017), 224-239.Dynamical correspondences for Smale spaces
With Robin Deeley and Brady Killough
New York Journal of Math, 22 (2016), 943-988.Fractal dual substitution tilings
With Natalie Priebe Frank and Samuel Webster
Journal of Fractal Geometry, 3 (2016), 265-317.Functorial properties of Putnam's homology theory for Smale spaces
With Robin Deeley and Brady Killough
Ergodic Theory and Dynamical Systems, 36 (2016), 1411-1440.Topological spaces associated to higher-rank graphs
With Alex Kumjian, David Pask and Aidan Sims
Journal of Combinatorial Theory, Series A, 143 (2016), 19-41.Twisted C*-algebras associated to finitely aligned higher-rank graphs
With Aidan Sims and Ben Whitehead
Documenta Mathematica, 19 (2014), 831-866.Equilibrium states on the Cuntz-Pimsner algebras of self-similar actions
With Marcelo Laca, Iain Raeburn and Jacqui Ramagge
The Journal of Functional Analysis, 266 (2014), 6619-6661.Zappa-Szép products of semigroups and their C*-algebras
With Nathan Brownlowe, Jacqui Ramagge, and Dave Robertson
The Journal of Functional Analysis, 266 (2014), 3937-3967.Cohomology of the Pinwheel tiling
With Dirk Frettlöh and Ben Whitehead
Journal of the Australian Math Society, 97 (2014), 162-179.Spectral triples for hyperbolic dynamical systems
The Journal of Noncommutative Geometry, 7 (2013), 563-582.A fractal version of the Pinwheel tiling
With Natalie Priebe Frank
The Mathematical Intelligencer, 33 (2011), 7-17.C*-algebras of tilings with infinite rotational symmetry
The Journal of Operator Theory 64 (2010), 299-319.
Theses:
Poincaré duality and spectral triples for hyperbolic dynamical systems PhD Thesis (2010)
Groupoid C*-algebras of the Pinwheel tiling Master's Thesis (2005)
Unpublished and other works:
Classification of tiling C*-algebras
With Luke J. Ito and Joachim Zacharias