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Continuum Schrödinger operators associated with aperiodic subshifts (with Jake Fillman and Anton Gorodetski), Ann. Henri Poincaré 15 (2014), 1123-1144 (This paper was awarded the 2014 Annales Henri Poincaré Prize.) Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians (with Anton Gorodetski), Commun. Math. Phys. 337 (2015), 1241-1253 The Fibonacci Hamiltonian (with Anton Gorodetski and William Yessen), Invent. Math. 206 (2016), 629-692

Almost-periodicity in time of solutions of the Toda lattice (with Ilia Binder, Milivoje Lukic, and Tom VandenBoom), C. R. Math. Rep. Acad. Sci. Canada 40 (2018), 1-28 Must the spectrum of a random Schrödinger operator contain an interval? (with Anton Gorodetski), Commun. Math. Phys. 393 (2022), 1583-1613.The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations (with Michael Goldstein and Milivoje Lukic), Invent. Math. 207 (2017), 895-980 Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian (with Anton Gorodetski), Commun. Math. Phys. 323 (2013), 497-515 Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients (with Licheng Fang, Shuzheng Guo), J. Funct. Anal. 279 (2020), 108803, 22 pp

Subordinacy theory for extended CMV matrices (with Shuzheng Guo, Darren Ong), Sci. China Math. 65 (2022), 539-558. The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous (with Michael Goldstein and Milivoje Lukic), J. Spectr. Theory 6 (2016), 415-427 Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line (with Daniel Lenz), Israel J. Math. 247 (2022), 783-796 Singular density of states measure for subshift and quasi-periodic Schrödinger operators (with Artur Avila and Zhenghe Zhang), Commun. Math. Phys. 330 (2014), 469-498 Schrödinger operators generated by locally constant functions on the Fibonacci subshift (with Licheng Fang, Hyunkyu Jun), Ann. Henri Poincaré 22 (2021), 1459-1498Schrödinger operators with potentials generated by hyperbolic transformations: I. Positivity of the Lyapunov exponent (with Artur Avila, Zhenghe Zhang), Invent. Math. 231 (2023), 851-927.

Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients (with Long Li, Qi Zhou), Trans. Amer. Math. Soc. 375 (2022), 6093-6125Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum (with Jake Fillman and Milivoje Lukic), J. Spectr. Theory 7 (2017), 1101-1118 Multidimensional Schrödinger operators whose spectrum features a half line and a Cantor set (with Jake Fillman, Anton Gorodetski), J. Funct. Anal. 280 (2021), 108911, 38 pp Random Sturm-Liouville operators with generalized point interactions (with Rafael del Rio, Asaf L. Franco), Oper. Matrices 14 (2020), 1101-1125 Random Hamiltonians with arbitrary point interactions in one dimension (with Jake Fillman, Mark Helman, Jacob Kesten, Selim Sukhtaiev), J. Differential Equations 282 (2021), 104-126 Open problems and conjectures related to the theory of mathematical quasicrystals (with Faustin Adiceam, Franz Gähler, Uwe Grimm, Alan Haynes, Antoine Julien, Andrés Navas, Lorenzo Sadun and Barak Weiss), Arnold Math. J. 2 (2016), 579-592

Characterizations of uniform hyperbolicity and spectra of CMV matrices (with Jake Fillman, Milivoje Lukic, and William Yessen), Discrete Contin. Dyn. Syst. S 9 (2016), 1009-1023Transport exponents of Sturmian Hamiltonians (with Anton Gorodetski, Qinghui Liu, and Yanhui Qu), J. Funct. Anal. 269 (2015), 1404-1440 Simon's OPUC Hausdorff dimension conjecture (with Shuzheng Guo, Darren Ong), Math. Ann. 384 (2022), 247-283