Research
Research interests
Mathematical Physics, Harmonic Analysis, Quantum walk, Dynamical Systems and Ergodic Theory
Here is a link to my arXiv papers.
Preprints
On the spectrum of magnetic Laplacian on the Lieb lattice. arxiv.org/abs/2401.11405 (joint with M. G. Solis and D. Spedale)
Second phase transition line: a constructive proof. (joint with S. Jitomirskaya and Q. Zhou)
Phase transition in phase: the interface. (joint with S. Jitomirskaya)
Anti-resonances and sharp analysis of Maryland localization for all parameters. (joint with R. Han, S. Jitomirskaya)
Accepted and Published Papers
Anderson localization for the Unitary Almost Mathieu operator. arxiv.org/abs/2201.05779, Nonlinearity, to appear.
Decay of multi-point correlation functions in $Z^d$. (joint with R. Han) Communications in Mathematical Physics, 405, no. 2 (2024): 45.
A Polynomial Roth Theorem for Corners in Finite Fields. (joint with R. Han, M. T. Lacey), Mathematika 67.4 (2021): 885-896.
Averages along the Square Integers: $\ell^p$ improving and Sparse Inequalities. (joint with R. Han, M. T. Lacey)
Tunisian Journal of Mathematics, Vol. 3 (2021), No. 3, pp. 517–550, 2021
Pure point spectrum for the Maryland model: A constructive proof. (joint with S. Jitomirskaya),
Ergodic Theory and Dynamical Systems, (2021) 41(1), 283-294.
Improving estimates for discrete polynomial averages. (joint with R. Han, V. Kovač, M. T. Lacey, J. Madrid),
J Fourier Anal Appl 26, 42 (2020).
Averages Along the Primes: Improving and Sparse Bounds. (joint with R. Han, B. Krause, M. T. Lacey),
Concrete Operators, (2020) 7(1), 45-54.
(joint with R. Han and S. Zhang), Journal d'Analyse Mathématique, 142.2 (2020): 605-666.
Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasi-periodic Schrödinger operators. (joint with S. Zhang), Ann. Henri Poincaré, 20(7), pp. 2481–2494, 2019.
Spectral transition line for the extended Harper's model in the positive Lyapunov exponent regime.
Journal of Functional Analysis, 275(3), pp.712-734, 2018
Generic continuous spectrum for multi-dimensional quasiperiodic Schrödinger operators with rough potentials. (joint with R. Han), Journal of Spectral Theory, 8(4), pp. 1635–1645, 2018.
Singular continuous spectrum for singular potential, (joint with S. Jitomirskaya), Communications in Mathematical Physics, 351(3), pp.1127-1135, (2017).
Papers in preparation
Universal hierarchical structure of eigenfunctions of the Maryland model. (joint with R. Han, S. Jitomirskaya)
Talks
The seventh Great Lakes Mathematical Physics Meeting, Oberlin College, OH, June 9-11, 2023
Special session on Spectral Theory at the AMS Sectional Meeting, Georgia Tech, March 18 -19, 2023
Workshop "Almost-Periodic Spectral Problems", Banff International Research Station, Canada, April 17 - 22, 2022
Special session at AMS Sectional Meetings, Online, March 2022
Colloquium, Louisiana State University, January 20, 2022
Applied analysis seminar, LSU, November 22, 2021
Minisymposium at the 4th Annual Meeting of SIAM TX-LA Section, South Padre Island, Texas, November 2021
Webinar on Analysis and PDE, October 8, 2021
(canceled) New directions in disordered systems, Cergy, France, June 28 - July 3rd 2020
(canceled) 37th Western States Mathematical Physics Meeting, UC Irvine, March 2020
Colloquium, University of Oklahoma, Jan 3, 2020
Mathematical Physics at the Crossings. Celebrating the 65th Birthday of George Hagedorn, Virginia Tech, May 2019
AMS Special Session on "Localization and Delocalization for Disordered Quantum Systems", Baltimore Convention Center, January 18-19, 2019
Georgia Tech Math Physics Seminar, "Transition lines for Almost Mathieu Operator", Nov 7, 2018
AMS Special Session "Ergodic and topological quantum systems", Ann Arbor, October 20-21, 2018
Joint Mathematics Meetings, San Diego, Jan 10-13, 2018.
AMS Special Session on "Analysis and Geometry of Fractals", UC Riverside, Nov 2017
UCI Math Physics Seminar: "Spectral transition line for the extended Harper's model", July 9, 2017
Dynamical System seminar, Nanjing University, China, April 25, 2017
35th Annual Western States Mathematical Physics Meeting, Caltech, Feb 12-13, 2017
Great Lakes Mathematical Physics Meeting, MSU, East Lansing, MI, June 17-19, 2016
Simons Center's Workshop: Between Dynamics and Spectral Theory, Simons Center for Geometry and Physics, Stony Brook, NY, June 2016
UCI Math Physics Seminar: "Singular continuous spectrum for singular potentials", Jan 7, 2016
Conferences attended
QMATH 15, Davis, California, Sep 12-16 2022, UC DAVIS
Almost-Periodic Spectral Problems, BIRSWorkshop, Alberta, Canada. April 12 - 17, 2020
Spectral Theory of Quasi-Periodic and Random Operators, CRM, Montreal, November 12-16, 2018.
Great Lakes Mathematical Physics Meeting, MSU, East Lansing, MI, June 23-25, 2017
Conference in Celebration of the 90th Anniversary of Mathematics Department of Tsinghua University, Tsinghua, April 22-24, 2017.
Introductory Workshop: Harmonic Analysis, January 23-27, 2017, MSRI, Berkeley.
Autumn School and Workshop: Discrete Schrödinger Operators and Quasi-Periodic Systems, Tsinghua University, Beijing, November 12-16, 2016.
Frontiers in Mathematical Physics, CRM, Université de Montréal, Canada, August–September 2016.
Young Researchers Symposium "Methods of Modern Mathematical Physics", Fields Institute, Toronto, Canada, August 2016.
Great Lakes Mathematical Physics Meeting, The Institute of Mathematical and Theoretical Physics of MSU, East Lansing, MI, June 17-19, 2016
Simons Center's Workshop: Between Dynamics and Spectral Theory, Simons Center for Geometry and Physics, Stony Brook, NY, June 5-10, 2016
Analysis and Beyond: Celebrating Jean Bourgain's Work and Impact, IAS, Princeton, NJ, May 21-24, 2016
34th Annual Western States Mathematical Physics Meeting, Caltech, Pasadena, CA, Feb 16-17, 2016
AMS Fall Western Sectional Meeting, Fullerton, CA, Oct 24-25, 2015
33rd Annual Western States Mathematical Physics Meeting, Caltech, Pasadena, CA, Feb 16-17, 2015