Research

Research Interest: 

Mathematical Physics, Harmonic Analysis, Dynamical Systems and Ergodic Theory

Publications:


Decay of multi-point correlation functions in Z^d.

Joint work with Fan Yang. CMP, volume 405, article number 45, (2024).


Decay of Information for the Kac Evolution

Joint work with Federico Bonetto and Michael Loss. Annales Henri Poincare. 2021, 22 (9), 2975-2993.


Honeycomb structures in magnetic fields

Joint work with Simon Becker, Svetlana Jitomirskaya and Maciej Zworski. J. Phys. A Math. Theor. (2021)


Density of states and Delocalization for discrete magnetic random Schrödinger operators

Joint work with Simon Becker. IMRN. 2022(17), 13447-13504.


Cantor spectrum of graphene in magnetic fields.

Joint work with Simon Becker and Svetlana Jitomirskaya. Invent. Math. 218 (2019).


Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle.

Joint work with Marius Lemm and Wilhelm Schlag. JST. 2020, 10 (4), 1139-1172


Discrete Bethe-Sommerfeld conjecture for triangular, square, and hexagonal lattices.

Joint work with Jake Fillman. Journal d'Analyse Math. 2020, 142 (1), 271-321


Spectral Dimension for β-almost periodic singular Jacobi operators and the extended Harper's model.

Joint work with Fan Yang and Shiwen Zhang. Journal d'Analyse Math. 2020, 142 (2), 605-666


Continuity of measure of the spectrum for Schrödinger operators with potentials defined by shifts and skew-shifts on higher dimensional tori.

Preprint.


Large deviation estimates and Hölder regularity of the Lyapunov exponent for analytic quasi-periodic Schrödinger cocycles.

Joint work with Shiwen Zhang. IMRN. 2022 (3), 1666-1713,


Effective multi-scale approach to the Schrödinger cocycle over a skew shift base.

Joint work with Marius Lemm and Wilhelm Schlag. ETDS. 2020, 40 (10), 2788-2853,


Shnol's theorem and the spectrum of long range operators.

Proc. Amer. Math. Soc., 147 (7), (2019).


Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy.

Joint work with Svetlana Jitomirskaya, Analysis and PDE, 12 (4), (2018).


Discrete Bethe-Sommerfeld Conjecture.

Joint work with Svetlana Jitomirskaya, CMP, 361(1), 2018.


Large coupling asymptotics of the Lyapunov exponent for quasi-periodic Schrödinger operators with analytic potentials.

Joint work with Christoph Marx, Annales Henri Poincare, 19 (1), (2018).


Full measure reducibility and localization for quasi-periodic Jacobi operators: a topological criterion.

Joint work with Svetlana Jitomirskaya, Adv. Math., 319 (2017), 224-250.


Generic continuous spectrum for multi-dimensional quasi periodic Schrödinger operators with rough potentials.

Joint work with Fan Yang, JST, 8(4), (2018).


Absence of point spectrum for the self-dual extended Harper's model.

IMRN, 9 (2018), 2801-2809


Dry Ten Martini Problem for the non-self-dual extended Harper's model.

Trans. Amer. Math. Soc. 370 (2018), 197-217.


Uniform localization is always uniform.

Proc. Amer. Math. Soc. 144 (2016), 609-612.



A Polynomial Roth Theorem for Corners in Finite Fields

Joint work with Michael T. Lacey and Fan Yang. Mathematika.2021, 67 (4), 885-896.


Improving Estimates for Discrete Polynomial Averages

Joint work with Vjekoslav Kovač, Michael T. Lacey, José Madrid, and Fan Yang. JFAA, 26, Article number: 42 (2020).


Averages along the primes: improving and sparse bounds.

Joint work with Ben Krause, Michael T. Lacey and Fan Yang,  Concrete Operators 7 (1), 45-54.


Averages along the square integers: $\ell^p$ improving and sparse inequalities.

Joint work with Michael T. Lacey and Fan Yang, Tunisian J. Math. 2021, 1 (1), 517


Weighted estimates for one sided martingale transforms.

Joint work with Wei Chen and Michael Lacey. Proc. AMS., 148 (2020).


A higher dimensional Bourgain-Dyatlov fractal uncertainty principle.

Joint work with Wilhelm Schlag. Analysis and PDE, Vol. 13 (2020), No. 3.