Chern Institute of Mathematics,NanKai University
Tianjin, China,300071
Room 603
Email:qizhou@nankai.edu.cn
Education
1. B.S. Soochow University, 2003-2007.
2. Ph.D. Nanjing University, 2007-2012. (Advisor: Jiangong You)
Position
1. Postdoctoral fellow at LPMA (UPMC), 09/2012-08/2014 Supervisor: Raphael Krikorian.
2. Postdoctoral fellow at Universite Paris Diderot, CNRS, 09/2014--08/2015 Supervisor: Artur Avila.
3. Visiting Scholar, University of California, Irvine, 09/2015-12/2015.
4. Professor, Nanjing University, Deng Feng Scholar Program B, 01/2016-08/2019
5. Professor, Nankai University, 09/2019--
Research
1. Reducibility results for quasi-periodic cocycles with Liouvillean frequency(with J.Wang), Journal of Dynamics and Differential Equations, Volume 24, Issue 1, pp 61-83, 2012.
2. Simultaneous Linearization for commuting quasi-periodically forced circle diffeomorphisms(with J.Wang), Proceedings of the AMS, Volume 141, Number 2, 625-636, 2013.
3. Embedding of analytic quasi-periodic cocycles into analytic quasi-periodic linear systems and its applications(with J.You) Communications in Mathematical Physics, 323, 975-1005, 2013
4. Phase transition and semi-global reducibility (with J.You). Communications in Mathematical Physics, Volume 330, Issue 3, 1095-1113, 2014.
5. Point Spectrum For Quasi-periodic Long Range Operators (with J.You and S. Zhang). Journal of spectral theory. Issue 3, 769-781, 2014.
6. Simple Counter-examples to Kotani-Last Conjecture via reducibility (with J. You). International Mathematics Research Notices. No. 19, 9450-9455, 2015
7. Response Solutions for Quasi-periodically Forced Harmonic Oscillators (with J.Wang, J.You). Transactions of the AMS， Volume 369, Number 6, June 2017, Pages 4251-4274
8. Sharp Phase transitions for the almost Mathieu operator (with A.Avila and J.You).Duke Math J，Volume 166, Number 14 (2017), 2697-2718.
9. Second phase transition line (with A. Avila and S. Jitomirskaya) Math Ann, Volume 370, Issue 1-2, 271-285, 2018
10. Linearization of quasi-periodically forced circle flow beyond Brjuno condition(with R.Krikorian, J.Wang, J.You). Comm. Math. Phys,358 (2018), no. 1, 81-100.
11. Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles (with A. Cai, C.Chavaudret and J.You) Math. Z.291 (2019), no. 3-4, 931-958.
12. Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator (with B.Helffer, Q.Liu, Y. Qu). Comm. Math. Phys. 368 (2019), no. 1, 369-382.
13. Genericity of mode-locking for quasiperiodically forced circle maps (with T.Jager, J. Wang). Adv. Math. 348 (2019), 353-377.
14. Quasi-periodic solutions of NLS with liouvillean frequency(with X.Xu, J.You) ANALYSIS & PDE Vol. 14 (2021), No. 8, 2327–2362, DOI: 10.2140/apde.2021.14.2327
15. Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrodinger operator(with X.Hou, J.Wang) Journal of Functional Analysis 279(6):108632
16. Exponential dynamical localization: Criterion and applications(with L.Ge,J.You) Annales scientifiques de l'ENS Article - Tome 56 - Fasc. 1 - pp 91-126 - 2023, DOI : 10.24033/asens.2529
17. 1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms(with Z.Liang,Z. Zhao) J. Math. Pures. Appl (9) 146 (2021)
18. One dimensional quasiperiodic mosaic lattice with exact mobility edges(with Y.Wang et al) Physical Review Letters 125:196604.
19. Anosov-Katok constructions for quasi-periodic $SL(2,R)$ cocycles (with N.Karaliolios, X.Xu) Peking Math J 7, 203–245 (2024). https://doi.org/10.1007/s42543-022-00056-y
20. Exact mobility edges, $PT$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals (with Y.Liu et al) Phys. Rev. B 103, 014203,2021
21. Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals（with Y.Liu and S.Chen）Phys. Rev. B 104, 024201,2021 (Editor's suggestion)
22. Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications (with H. Cheng, L.Ge,J.You) Advances in Mathematics, 19 November 2022, Volume 409, Part B, Article 108679
23. Absolutely Continuous Spectrum for CMV Operators With Small Quasi-Periodic Verblunsky Coefficients (with L.Li, D. Damanik) Trans. Amer. Math. Soc. 375 (2022), 6093-6125 10.1090/tran/8696
24. Traveling fronts for Fisher-KPP lattice equations in almost periodic media (with X.Liang, H.Wang and T. Zhou) Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 5, pp. 1179–1237, DOI 10.4171/AIHPC/101
25. Exact mobility edges for 1D quasiperiodic models (with Y. Wang, X. Xia, J.You, Z. Zheng) Commun. Math. Phys. 401, 2521–2567 (2023). https://doi.org/10.1007/s00220-023-04695-9
26. On the abominable properties of the almost Mathieu operator with well approximated frequencies(with A.Avila, Y. Last, M.Shamis) Duke Math. J. 173(4): 603-672 (15 March 2024). DOI: 10.1215/00127094-2023-0022
27. Quantitative almost reducibility and Mobius disjointness for analytic quasiperiodic Schrodinger cocycles(with W. Huang, J.Wang, Z.Wang) Peking Math J (2023). https://doi.org/10.1007/s42543-023-00081-5
28. Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients(with L.Li, D. Damanik) Journal of Functional Analysis, 15 December 2022, Volume 283, Issue 12, Article 109709
29. Stability of Spectral Types of Quasi-periodic Schrödinger Operators with Respect to Perturbations by Decaying Potentials (with Damanik, D., Li, X., You, J). Commun. Math. Phys.403, 1069–1108 (2023).
30. Exact New Mobility Edges between Critical and Localized States.(with Zhou, Xin-Chi and Wang, Yongjian and Poon, Ting-Fung Jeffrey and Liu, Xiong-Jun) Phys. Rev. Lett. 131, 176401 (2023)
31. Christopher Cedzich, Jake Fillman, Long Li, Darren C Ong, Qi Zhou, Exact Mobility Edges for Almost-Periodic CMV Matrices via Gauge Symmetries, International Mathematics Research Notices, Volume 2024, Issue 8, April 2024, Pages 6906–6941.
32. Xueyin Wang, Zhenfu Wang, Jiangong You, Qi Zhou, Winding Number, Density of States, and Acceleration, International Mathematics Research Notices, Volume 2024, Issue 9, May 2024, Pages 7972–7997.
33. Zhenguo Liang, Zhiyan Zhao, Qi Zhou. Almost reducibility and oscillatory growth of Sobolev norms. Advances in Mathematics, Volume 436, January 2024, 109417.
34. Xueyin Wang, Jiangong You, Qi Zhou, Isospectrum of non-self-adjoint almost-periodic Schrödinger operators . J. Spectr. Theory 14 (2024), no. 1, pp. 355–396
35. Zhenfu Wang, Jiangong You, Qi Zhou. Non-self-adjoint quasi-periodic operators with complex spectrum. Journal of Functional AnalysisVolume 287, Issue 10, 15 November 2024, 110614
36. Xuanji Hou, Yi Pan, Qi Zhou Dynamical classification of analytic one-frequency quasi-periodic SO(3,R) cocycles. Advances in Mathematics, Volume 457, November 2024, 109943
37. Asymptotics of spectral gaps of quasi-periodic Schrodinger operators (with M. Leguil,J. You, Z. Zhao). To appear in Cambridge J Math.
38. Xueyin Wang, Zhenfu Wang, Jiangong You, Qi Zhou.Spectrum of Hatano-Nelson model with strictly ergodic potentials.To appear in Journal d'Analyse Math\'ematique.
