Publications and Preprints
“Flow views and infinite interval exchange transformations for recognizable substitutions”, preprint, 2023.
“Spectral theory of spin substitutions” (with Neil Manibo), Discrete and Continuous Dynamical Systems 42, no. 11 (2022).
“Three variations on a theme by Fibonacci”, Stochastics and Dynamics 21, no. 3 (2021). This was a “top downloaded paper” for this journal in 2021.
“Geometric properties of a non-Pisot inflation and absence of absolutely continuous spectrum” (with Michael Baake, Uwe Grimm, and E. Arthur Robinson, Jr.), Studia Mathematica 247, no. 2 (2019), 109-154.
“An introduction to hierarchical tiling dynamical systems“, Lecture Notes from the Jean-Morlet Chair, Centre International de Rencontres Mathematiques, November 2017. To appear in Springer’s Lecture Notes in Mathematics.
“Fractal dual substitution tilings” (with Michael F. Whittaker and Samuel Webster), Journal of Fractal Geometry 3, no. 3 (2016), pp. 265-317.
“Tilings with infinite local complexity”, in J. Kellendonk, D. Lenz, and J. Savinien, editors, Mathematics of Aperiodic Order, Progress in Mathematics 309, Birkhauser, 2015.
“Fusion: a general framework for hierarchical tilings”, in the Proceedings of the 12th International Conference on Quasicrystallography (ICQ12), Acta Physica Polonica A 126 (2014), pp. 461-466.
“Fusion tilings with infinite local complexity” (with Lorenzo Sadun), Topology Proceedings 43 (2014), pp. 235-276.
“Fusion: a general framework for hierarchical tilings of R^d” (with Lorenzo Sadun), Geometriae Dedicata, Online First 2013. DOI: 10.1007/s10711-013-9893-7. Print version: 171, no. 1 (2014), pp. 149-186.
“A fractal version of the pinwheel tiling” with Michael F. Whittaker (downloadable preprint). Mathematical Intelligencer 33, no. 2 (2011), pp. 7 – 17. Here’s a view-only link to the published version.
“A dynamical system using the Voronoi tessellation” (with Sean Hart), American Mathematical Monthly 117, no. 2 (2010), pp. 99-112.
“Spectral theory of bijective substitution sequences” Oberwolfach Reports 6 (2009), no. 1, somewhere in pp. 725-766. This is an extended abstract of my March 5, 2009 talk at Oberwolfach.
“Topology of (some) tiling spaces without finite local complexity” (with Lorenzo Sadun), Discrete Contin. Dyn. Syst. 23 (2009), no. 3, 847-865.
“A primer of substitution tilings of the Euclidean plane” Expo. Math. 26 (2008), no. 4, 295-326.
“Generalized beta-expansions, substitution tilings, and local finiteness” (With E. A. Robinson, Jr.) Trans. Amer. Math. Soc. 360 (2008), no. 3, 1163-1177.
“Multidimensional constant-length substitution sequences”
Topology and its Applications 152, no. 1-2: 44-69, 2005.
Proceedings of the Dynamical Systems Conference.
“Detecting combinatorial hierarchy in tilings using derived Voronoi tessellations”
Discrete and Computational Geometry 29: 459-476, 2003. Here is a link to the published version, which I think is open access now.
“Substitution sequences in Z^d with a nonsimple Lebesgue component in the spectrum”.
Ergodic Theory and Dynamical Systems 23, no 2: 519-532, 2003.
“Characterization of planar pseudo-self-similar tilings” (with Boris Solomyak),
Discrete and Computational Geometry 26, no. 3: 289-306, 2001. Here is a link to the published version, which I think is open access now.
“Towards a characterization of self-similar tilings via derived Voronoi tessellations”
Geometriae Dedicata 79: 239-265, 2000. Here’s a link to the published version, which I think is open access now.
Undergraduate Research Summer Institute technical report (unpublished), with Allison Edgren, Olivia Gillham, and Sean Hart: “On a dynamical system based on Voronoi tessellations”