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Uniform hyperbolicity for Szego cocycles and applications to random CMV matrices and the Ising model (with Jake Fillman, Milivoje Lukic, and William Yessen), Int. Math. Res. Not. 2015 (2015), 7110-7129 New anomalous Lieb-Robinson bounds in quasiperiodic XY chains (with Marius Lemm, Milivoje Lukic and William Yessen), Phys. Rev. Lett. 113 (2014), 127202

Limit-periodic continuum Schrödinger operators with zero measure Cantor spectrum (with Jake Fillman and Milivoje Lukic), J. Spectr. Theory 7 (2017), 1101-1118 The Fibonacci Hamiltonian (with Anton Gorodetski and William Yessen), Invent. Math. 206 (2016), 629-692 One-Dimensional Ergodic Schrödinger Operators, I. General Theory (with Jake Fillman), Graduate Studies in Mathematics 221, American Mathematical Society, 2022. He can also appear while Temple Trekking, during which he enchants the player with the power of water, and the player must put out the fires surrounding his grotto.Must the spectrum of a random Schrödinger operator contain an interval? (with Anton Gorodetski), Commun. Math. Phys. 393 (2022), 1583-1613. Multidimensional almost-periodic Schrödinger operators with Cantor spectrum (with Jake Fillman and Anton Gorodetski), Ann. Henri Poincaré 20 (2019), 1393-1402 Transport 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

Limit-periodic Schrödinger operators with Lipschitz continuous IDS (with Jake Fillman), Proc. Amer. Math. Soc. 147 (2019), 1531-1539 The almost sure essential spectrum of the doubling map model is connected (with Jake Fillman), Commun. Math. Phys. 400 (2023), 793-804.

Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients (with Long Li, Qi Zhou), J. Funct. Anal. 283 (2022), Paper No. 109709 Limit-periodic Schrödinger operators on Z Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent (with Valmir Bucaj, Jake Fillman, Vitaly Gerbuz, Tom VandenBoom, Fengpeng Wang, Zhenghe Zhang), Trans. Amer. Math. Soc. 372 (2019), 3619-3667 The spectrum of Schrödinger operators with randomly perturbed ergodic potentials (with Artur Avila, Anton Gorodetski), Geom. Funct. Anal. 33 (2023), 364-375. On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data (with Michael Goldstein), J. Amer. Math. Soc. 29 (2016), 825-856Schrödinger operators with dynamically defined potentials, Ergodic Theory Dynam. Systems 37 (2017), 1681-1764 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 A multi-scale analysis scheme on Abelian groups with an application to operators dual to Hill's equation (with Michael Goldstein and Milivoje Lukic), Trans. Amer. Math. Soc. 369 (2017), 1689-1755 Lyapunov exponents: recent applications of Furstenberg's theorem in spectral theory, MATRIX Annals, MATRIX Book Ser. 4, Springer, Cham (2021), 685--689 Schrödinger operators with potentials generated by hyperbolic transformations: I. Positivity of the Lyapunov exponent (with Artur Avila, Zhenghe Zhang), Invent. Math. 231 (2023), 851-927.