Research

Preprints:

• Katsura's self-similar groupoid actions, Putnam's binary factors, and their limit spaces
  With Jeremy Hume

• C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
  With Zahra Afsar, Nathan Brownlowe and Jacqui Ramagge
  to appear in the Journal of Operator Theory.

In print:

• Self-similarity and limit spaces of substitution tiling semigroups
  With Jamie Walton
  Groups, Geometry, and Dynamics, 18 (2024), 1201–1231.

• KK-duality for self-similar groupoid actions on graphs
  With Nathan Brownlowe, Alcides Buss, Daniel Gonçalves, Jeremy B. Hume, and Aidan Sims
  Transactions of the American Mathematical Society, 377 (2024), 5513-5560.

• A geometric representative for the fundamental class in KK-duality of Smale spaces
  With Dimitris Gerontogiannis and Joachim Zacharias
  Journal of Functional Analysis, 287 (2024), 1-49.

• Planar aperiodic tile sets: from Wang tiles to the Hat and Spectre monotiles
  With Tinka Bruneau
  Nieuw Archief voor Wiskunde, 24 (2023), 207-214.

• An aperiodic tile with edge-to-edge orientational matching rules
  With Jamie Walton
  Journal of the Institute of Mathematics of Jussieu, 22 (2023), 1727-1755.

• 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