Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian (with Anton Gorodetski), Israel J. Math. 206 (2015), 109-126 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 Characterizations of uniform hyperbolicity and spectra of CMV matrices (with Jake Fillman, Milivoje Lukic, and William Yessen), Discrete Contin. Dyn. Syst. S 9 (2016), 1009-1023 Cantor spectrum for CMV matrices with almost periodic Verblunsky coefficients (with Long Li, Qi Zhou), J. Funct. Anal. 283 (2022), Paper No. 109709 The isospectral torus of quasi-periodic Schrödinger operators via periodic approximations (with Michael Goldstein and Milivoje Lukic), Invent. Math. 207 (2017), 895-980

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 Lyapunov exponents: recent applications of Furstenberg's theorem in spectral theory, MATRIX Annals, MATRIX Book Ser. 4, Springer, Cham (2021), 685--689 Johnson-Schwartzman gap labelling for ergodic Jacobi matrices (with Jake Fillman, Zhenghe Zhang), J. Spectr. Theory 13 (2023), 297-318. 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), 3619-3667Spectral transitions for the square Fibonacci Hamiltonian (with Anton Gorodetski), J. Spectr. Theory 8 (2018), 1487-1507 Anderson localization for quasi-periodic CMV matrices and quantum walks (with Fengpeng Wang), J. Funct. Anal. 276 (2019), 1978-2006 Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians (with Anton Gorodetski), Commun. Math. Phys. 337 (2015), 1241-1253 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), 825-856

Transport exponents of Sturmian Hamiltonians (with Anton Gorodetski, Qinghui Liu, and Yanhui Qu), J. Funct. Anal. 269 (2015), 1404-1440 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 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), 1-28Homogeneity of the spectrum for quasi-periodic Schrödinger operators (with Michael Goldstein, Wilhelm Schlag, Mircea Voda), J. Eur. Math. Soc. 20 (2018), 3073-3111 Schrödinger operators with dynamically defined potentials, Ergodic Theory Dynam. Systems 37 (2017), 1681-1764 Random Sturm-Liouville operators with generalized point interactions (with Rafael del Rio, Asaf L. Franco), Oper. Matrices 14 (2020), 1101-1125 An extension of the Kunz-Souillard approach to localization in one dimension and applications to almost-periodic Schrödinger operators (with Anton Gorodetski), Adv. Math. 297 (2016), 149-173 Simon's OPUC Hausdorff dimension conjecture (with Shuzheng Guo, Darren Ong), Math. Ann. 384 (2022), 247-283

One-Dimensional Ergodic Schrödinger Operators, I. General Theory (with Jake Fillman), Graduate Studies in Mathematics 221, American Mathematical Society, 2022. Limit-periodic Schrödinger operators with a discontinuous Lyapunov exponent (with Zheng Gan, Helge Krüger), J. Funct. Anal. 279 (2020), 108565, 16 pp Limit-periodic Schrödinger operators with Lipschitz continuous IDS (with Jake Fillman), Proc. Amer. Math. Soc. 147 (2019), 1531-1539 Localization for Anderson models on metric and discrete tree graphs (with Jake Fillman, Selim Sukhtaiev), Math. Ann. 376 (2020), 1337-1393

Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients (with Licheng Fang, Shuzheng Guo), J. Funct. Anal. 279 (2020), 108803, 22 pp Anderson localization for radial tree graphs with random branching numbers (with Selim Sukhtaiev), J. Funct. Anal. 277 (2019), 418-433 Szego's theorem for canonical systems: the Arov gauge and a sum rule (with Benjamin Eichinger, Peter Yuditskii), J. Spectr. Theory 11 (2021), 1255-1277 Subordinacy theory for extended CMV matrices (with Shuzheng Guo, Darren Ong), Sci. China Math. 65 (2022), 539-558.

Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients (with Long Li, Qi Zhou), Trans. Amer. Math. Soc. 375 (2022), 6093-6125Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces (with Peter Yuditskii), Adv. Math. 293 (2016), 738-781 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.) Must the spectrum of a random Schrödinger operator contain an interval? (with Anton Gorodetski), Commun. Math. Phys. 393 (2022), 1583-1613. Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian (with Anton Gorodetski), Commun. Math. Phys. 323 (2013), 497-515 Almost periodicity in time of solutions of the KdV equation (with Ilia Binder, Michael Goldstein, Milivoje Lukic), Duke Math. J. 167 (2018), 2633-2678