I am currently a Hale Visiting Assistant Professor at Georgia Institute of Technology.
Email: rui dot han at math dot gatech dot edu.
This is my CV (updated Oct 21, 2019).
Research interests

Mathematical Physics: Anderson localization, BetheSommerfeld conjecture, Kinetic theory, Quantum dynamics, Quantum Hall effects, Spectral theory for ergodic Schrödinger operators, Spectral theory for random Schrödinger operators.
Harmonic Analysis: Fractal uncertainty principle, Sparse domination, Weighted inequality
Dynamical Systems and Ergodic Theory: Positivity and regularity of Lyapunov exponent
Academic Position
 Institute for Advanced Study
Member, September 2017 July 2018
Education
 University of California, Irvine
Ph.D. Mathematics, September 2012 June 2017Advisor: Svetlana Jitomirskaya
 University of Science and Technology of China
B.S. Mathematics, School of Gifted Young, 20082012
Grants and Awards
 NSF DMS1800689, 20182021
 Kovalevsky Outstanding Ph.D. Thesis Award (UC Irvine), 2017
 Von Neumann Award for outstanding performance (UC Irvine), 2016
 Connelly Award for maintaining an excellent record of teaching and research (UC Irvine), 2014
Publications
21. $\ell^p$improving estimates for discrete polynomial averages via bounds for exponential sums.
Joint work with Vjekoslav Kovač, Michael T. Lacey, José Madrid, and Fan Yang, preprint.20. Averages along the primes: improving and sparse bounds.
Joint work with Ben Krause, Michael T. Lacey and Fan Yang, preprint.19. Averages along the square integers: $\ell^p$ improving and sparse inequalities.
Joint work with Michael T. Lacey and Fan Yang, submitted.18. Weighted estimates for one sided martingale transforms.
Joint work with Wei Chen and Michael Lacey. Proc. AMS., to appear.17. A higher dimensional BourgainDyatlov fractal uncertainty principle.
Joint work with Wilhelm Schlag. Analysis and PDE, to appear.16. Cantor spectrum of graphene in magnetic fields.
Joint work with Simon Becker and Svetlana Jitomirskaya. Invent. Math., to appear.15. Weyl sums and the Lyapunov exponent for the skewshift Schrödinger cocycle.
Joint work with Marius Lemm and Wilhelm Schlag. JST, to appear.14. Discrete BetheSommerfeld conjecture for triangular, square, and hexagonal lattices.
Joint work with Jake Fillman. Journal d'Analyse Math, to appear.13. Spectral Dimension for βalmost periodic singular Jacobi operators and the extended Harper's model.
Joint work with Fan Yang and Shiwen Zhang. Journal d'Analyse Math, to appear.11. Large deviation estimates and Hölder regularity of the Lyapunov exponent for analytic quasiperiodic Schrödinger cocycles.
Joint work with Shiwen Zhang. IMRN, to appear.10. Effective multiscale approach to the Schrödinger cocycle over a skew shift base.
Joint work with Marius Lemm and Wilhelm Schlag. ETDS, to appear.9. Shnol's theorem and the spectrum of long range operators.
Proc. Amer. Math. Soc., 147 (7), (2019).8. Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy.
Joint work with Svetlana Jitomirskaya, Analysis and PDE, 12 (4), (2018).7. Discrete BetheSommerfeld Conjecture.
Joint work with Svetlana Jitomirskaya, CMP, 361(1), 2018.6. Large coupling asymptotics of the Lyapunov exponent for quasiperiodic Schrödinger operators with analytic potentials.
Joint work with Christoph Marx, Annales Henri Poincare, 19 (1), (2018).5. Full measure reducibility and localization for quasiperiodic Jacobi operators: a topological criterion.
Joint work with Svetlana Jitomirskaya, Adv. Math., 319 (2017), 224250.4. Generic continuous spectrum for multidimensional quasi periodic Schrödinger operators with rough potentials.
Joint work with Fan Yang, JST, 8(4), (2018).3. Absence of point spectrum for the selfdual extended Harper's model.
IMRN, 9 (2018)2. Dry Ten Martini Problem for the nonselfdual extended Harper's model.
Trans. Amer. Math. Soc. 370 (2018), 197217.1. Uniform localization is always uniform.
Proc. Amer. Math. Soc. 144 (2016), 609612.
Harmonic analysis
Mathematical Physics
Papers in preparation
Universal hierarchical structure of eigenfunctions of the Maryland model.
Joint work with Svetlana Jitomirskaya and Fan YangMeasure of the spectrum of extended Harper's model.
Joint work with Svetlana Jitomirskaya