Research
Research Interests
Algebraic geometry, combinatorics and complex analysis in spectral theory of periodic operators
Spectral theory of Laplacians on non-compact Riemannian manifolds
Spectral theory of quasiperiodic Schrödinger operators
WKB type solutions and spectral theory of Schrödinger operators with decaying potentials
KAM theory in Hamiltonian PDEs
Transport theory in quantum physics
Fractal properties of singular continuous spectra
HRT conjecture, Littlewood conjecture and inhomogeneous Diophantine approximation
Publications
W. Liu. Fermi isospectrality for discrete periodic Schrodinger operators. Comm. Pure Appl. Math. 77 (2024), no. 2, 1126–1146. arXiv version
W. Liu. Small denominators and large numerators of quasiperiodic Schrodinger operators. Peking Math J to appear. arXiv version
W. Liu. Distributions of resonances of supercritical quasi-periodic operators. Int. Math. Res. Not. IMRN 2024, no. 1, 197--233. arXiv version
W. Liu. Bloch varieties and quantum ergodicity for periodic graph operators. J. Anal. Math. to appear. arXiv version
S. Jitomirskaya and W. Liu. Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transitions in phase. J. Eur. Math. Soc. (JEMS) to appear. arXiv version
J. Fillman, W. Liu, and R. Matos. Algebraic properties of the Fermi variety for periodic graph operators. J. Funct. Anal. 286 (2024), no. 4, Paper No. 110286. arXiv version
I. Kachkovskiy, W. Liu, and W-M Wang, Space-time quasi-periodic solutions to a nonlinear Schrodinger equation on $\Z$. J. Math. Phys. 65 (2024), no. 1, Paper No. 011502, 34 pp ( Special Collection: New Directions in Disordered Systems: In Honor of Abel Klein).
W. Liu. Floquet isospectrality for periodic graph operators. J. Differential Equations 374 (2023), 642--653. arXiv version
W. Liu and K. Lyu. One dimensional discrete Schrodinger operators with resonant embedded eigenvalues. From Complex Analysis to Operator Theory: A Panorama, 619--636, Oper. Theory Adv. Appl., 291, Birkhäuser/Springer, Cham, 2023. arXiv version
W. Liu. Fermi isospectrality of discrete periodic Schrodinger operators with separable potentials on $\Z^2$. Comm. Math. Phys. 399 (2023), no. 2, 1139--1149. arXiv version
W. Liu.Power law logarithmic bounds of moments for long range operators in arbitrary dimension. J. Math. Phys. 64 (2023), no. 3, Paper No. 033508, 11 pp ( Special Collection: New Directions in Disordered Systems: In Honor of Abel Klein). arXiv version
W. Liu. Quantitative inductive estimates for Green's functions of non-self-adjoint matrices. Anal. PDE 15 (2022), no. 8, 2061--2108. arXiv version
J. Fillman, W. Liu, and R. Matos. Irreducibility of the Bloch variety for finite-range Schrödinger operators. J. Funct. Anal. 283 (2022), no. 10, Paper No. 109670. arXiv version
W. Liu. Irreducibility of the Fermi variety for discrete periodic Schrodinger operators and embedded eigenvalues. Geom. Funct. Anal. 32 (2022), no. 1, 1--30. arXiv version
W. Liu. Topics on Fermi varieties of discrete periodic Schrodinger operators. J. Math. Phys. 63 (2022), no. 2, Paper No. 023503, 13 pp (Special Collection on the Proceedings of ICMP XX ). arXiv version
W. Liu. Criteria for embedded eigenvalues for discrete Schrödinger operators. Int. Math. Res. Not. IMRN 2021, no. 20, 15803--15832. arXiv version
W. Liu. Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrödinger operators. Nonlinearity 34 (2021), no. 3, 1288--1316. arXiv version
S. Jitomirskaya and W. Liu. Upper bounds on transport exponents for long range operators. Upper bounds on transport exponents for long-range operators. J. Math. Phys. 62 (2021), no. 7, Paper No. 073506, 9 pp (Special issue celebrating the work of Jean Bourgain). arXiv version
S. Jitomirskaya, H. Krüger, and W. Liu. Exact dynamical decay rate for the almost Mathieu operator. Math. Res. Lett. 27 (2020), no. 3, 789--808. arXiv version
W. Liu and D. Ong. Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators. J. Anal. Math.141 (2020), no. 2, 625--661. arXiv version
W. Liu. Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators. Math. Nachr. 293 (2020), no. 9, 1776--1790. arXiv version
S. Jitomirskaya and W. Liu. Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case. Trans. Amer. Math. Soc. 373 (2020), no. 8, 5885--5902. arXiv version
W. Liu. Almost Mathieu operators with completely resonant phases. Ergodic Theory Dynam. Systems 40 (2020), no. 7, 1875--1893. arXiv version
S. Jitomirskaya, W. Liu, and Y. Shi. Anderson localization for multi-frequency quasi-periodic operators on \Z^d. Geom. Funct. Anal. 30 (2020), no. 2, 457--481. arXiv version
W. Liu. Growth of the Eigensolutions of Laplacians on Riemannian Manifolds I: Construction of Energy Function. Int. Math. Res. Not. IMRN 2020, no. 9, 2561--2587. arXiv version
W. Liu. The Möbius transformation of continued fractions with bounded upper and lower partial quotients. Turkish J. Math. 44 (2020), no. 3, 813--824. arXiv version
S. Jitomirskaya, W. Liu, and S. Zhang. Arithmetic spectral transitions. IAS/Park City Mathematics Series: Harmonic Analysis and Applications (2020), vol. 27, 35--72.
W. Liu and Y. Shi. Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies. J. Spectr. Theory 9 (2019), no. 4, 1223--1248. arXiv version
W. Liu. The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators. Pure Appl. Funct. Anal. 4 (2019), no. 3, 589--602. arXiv version
S. Jitomirskaya and W. Liu. Inhomogeneous Diophantine approximation in the coprime setting. Adv. Math. 355 (2019), 106773. arXiv version
W. Liu. Some refined results on the mixed Littlewood conjecture for pseudo-absolute values. J. Aust. Math. Soc. 107 (2019), no. 01, 91--109. arXiv version
W. Liu. Letter to the Editor: Proof of the HRT conjecture for almost every (1,3) configuration. J. Fourier Anal. Appl. 25 (2019), no. 4, 1350--1360. arXiv version
W. Liu. Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators. J. Funct. Anal. 276 (2019), no. 9, 2936--2967. arXiv version
S. Jitomirskaya and W. Liu. Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian. Geom. Funct. Anal. 29 (2019), no. 1, 238--257. arXiv version
W. Liu. Absence of singular continuous spectrum for perturbed discrete Schrödinger operators. J. Math. Anal. Appl. 472 (2019), no. 2, 1420--1429. arXiv version
S. Jitomirskaya and W. Liu. Universal hierarchical structure of quasiperiodic eigenfunctions. Ann. of Math. (2) 187 (2018), no. 3, 721--776. arXiv version
W. Liu. Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of initial energy. Math. Phys. Anal. Geom. 21 (2018), no. 3, 21:18. arXiv version
W. Liu. Continuous quasiperiodic Schrödinger operators with Gordon type potentials. J. Math. Phys. 59 (2018), no. 6, 063501, 6 pp. arXiv version
S. Jitomirskaya and W. Liu. Arithmetic spectral transitions for the Maryland model. Comm. Pure Appl. Math. 70 (2017), no. 6, 1025--1051. arXiv version
S. Jitomirskaya and W. Liu. A Lower Bound on the Lyapunov Exponent for the Generalized Harper's Model. J. Stat. Phys. 166 (2017), no. 3-4, 609–617. arXiv version
W. Liu. The spectra of the surface Maryland model for all phases. Proc. Amer. Math. Soc. 144 (2016), no.12, 5035--5047. arXiv version
W. Liu and X. Yuan. Anderson localization for the completely resonant phases. J. Funct. Anal. 268 (2015), no. 3, 732--747. arXiv version
W. Liu and X. Yuan. Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime. J. Math. Phys. 56 (2015), no. 1, 012701, 21 pp. arXiv version
W. Liu and X. Yuan. Spectral gaps of almost Mathieu operators in the exponential regime. J. Fractal Geom. 2 (2015), no. 1, 1--51. arXiv version
W. Liu and X. Yuan. Anderson localization for the almost Mathieu operator in the exponential regime. J. Spectr. Theory 5 (2015), no. 1, 89--112. arXiv version
W. Liu and Z. Huang. On the relationship of the spectra of the self-adjoint operator and its Liouville operator. Internat. J. Theoret. Phys. 52 (2013), no. 8, 2578--2591.
W. Liu and Z. Huang. The generalized eigenvector expansions of the Liouville operator. Internat. J. Theoret. Phys. 52 (2013), no. 12, 4323--4334.
Preprints
W. Liu. Proof of geometric Borg's Theorem in arbitrary dimensions. arXiv version
W. Liu and W-M Wang. Nonlinear Anderson localized states at arbitrary disorder. arXiv version
M. Faust, W. Liu, R. Matos, J. Plute, J. Robinson, Y. Tao, E. Tran and C. Zhuang. Floquet isospectrality of the zero potential for discrete periodic Schrodinger operators. arXiv version
Notes
W. Liu. Sharp bound on the largest positive eigenvalue for one-dimensional Schrödinger operators. arXiv version
W. Liu and X. Yuan. Absolutely continuous spectra for quasiperiodic Schrödinger operators in the exponential regime. arXiv version
Conference Organizations
Special session "Periodicity in Quantum Systems" at the AMS Meeting, University of Texas, San Antonio, September 14-15, 2024 (with Long Li and Tal Malinovitch).
Session "Quantum Mechanics & Spectral Theory", ICMP, Strasbourg, France, July 1-6, 2024 (with Milivoje Lukic).
TXST Summer School in Mathematical Physics, Texas State University, June 3 to June 7, 2024 (with Jake Fillman).
TexAMP 2024, Texas A&M University, February 9–11, 2024.
BIRS Workshop "Randomness and Quasiperiodicity in Mathematical Physics", January 14–19, 2024 (with David Damanik, Constanza Rojas-Molina and Mira Shamis).
Special session "Spectral Methods in Quantum Systems", 2024 Joint Mathematics Meetings, San Francisco, CA, January 3-6, 2024 (with Matthew Powell).
Mini-Symposium "(Complex)analysis in differential equations", 2023 SIAM TX-LA Meeting, University of Louisiana at Lafayette, Louisiana, November 3-5, 2023 (co-organized with John Treuer).
Spectral Theory and Applications (we will also use the conference to celebrate Peter Kuchment and his contributions to the field), Texas A&M University, October 13–15, 2023.
Special session ''Disordered and Periodic Quantum Systems'' at the AMS Sectional Meeting, at Georgia Institute of Technology, March 18-19, 2023 (R. Matos and X. Zhu). Webpage
Mini-symposium at 5th Annual Meeting of the SIAM Texas-Louisiana Section, University of Houston, November 4th-6th, 2022 (with Rodrigo Matos and Fan Yang). Webpage
(Co-organizer) 2nd annual conference on spectral theory of differential operators, Nanjing, July 16-17, 2022.
(Co-organizer) 5th annual TX-LA undergraduate mathematics conference, University of Houston, March 26-27, 2022. Webpage
Special session ''Localization and delocalization in ergodic quantum systems'' at the AMS Sectional Meeting, San Francisco State University, 2021 (with I. Kachkovskiy and R. Matos). Webpage
Mini-symposium "Spectral theory and mathematical physics" at the third SIAM TX-LA Annual Meeting, Texas A&M university, 2020 (with J. Fillman). Webpage
36th Annual Western States Mathematical Physics Meeting, UC Irvine, CA, February 18 and 19, 2018 (with S. Jitomirskaya). Webpage
Colloquium Talks
The University of Texas Rio Grande Valley, April 19, 2024
University of Houston, Nov 29, 2023
Rice University, Sep 14, 2023
Special Colloquium, UC Irvine, Jan 8, 2019
Special Colloquium, UCLA, Jan 10, 2019
Special Colloquium, Texas A&M University, Jan 17, 2019
Special Colloquium, MSU, Jan 21, 2019
Special Colloquium, University of Arizona, Jan 31, 2019
Special Colloquium, Virginia Tech, February, 2019
Conference Talks
AMS Special Session "Spectral theory and quantum systems", Spring Sectional meeting, Howard University, Washington, DC, April 6-7, 2024
2024 CombinaTexas Conferences, Texas A&M University, March 23-24, 2024.
Brin MRC workshop - Mathematical Models of Electronic Transport and Phases in Low-Dimensional Material, University of Maryland, March 11-15, 2024
Mini-Symposium "Discrete and Continuous Schrodinger Operators", 2023 SIAM TX-LA Meeting, University of Louisiana at Lafayette, Louisiana, November 3-5, 2023
The Mathematics and Physics of Moire Superlattices, BIRS workshop, Banff, Canada, Oct 22-27, 2023.
2023 ICBS, Beijing, July 16-28, 2023
2023 CombinaTexas Conferences, Texas A&M University, April 22-23, 2023.
2023 Texas Differential Equations Conference, Texas State University-San Marcos, March 25, 2023.
Summer Informal Regional Functional Analysis Seminar (SUMIRFAS), Texas A&M University, July 29-31, 2022.
New directions in disordered systems on the occasion of the 75th birthday of Abel Klein, Cergy, France, June 27 - July 1, 2022.
2nd annual conference on spectral theory of differential operators, Nanjing, July 16-17, 2022.
Operator Theory Analysis and Mathematical Physics (OTAMP2022), Stockholm, Sweden, June 27-30, 2022.
Ergodic Operators and Quantum Graphs, Simon Center Workshop, Stony Brook, New York, June 6-10, 2022.
Baylor Analysis Fest "From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory", Baylor University, Waco, TX, May 23-27, 2022.
Workshop on KAM theory, Yangzhou University, May 8, 2022.
Almost-Periodic Spectral Problems, BIRS workshop, Banff, Canada, April 17-22, 2022.
Hyperbolic Dynamics and Structural Stability dedicated to 85th anniversary of Dmitry Anosov (1936-2014), Moscow, Russia, November 8–12, 2021.
The 4th Annual Meeting of the SIAM Texas Louisiana Section，University of Texas Rio Grande Valley, South Padre Island, TX, November 5-7, 2021.
Thematic Session "Quantum Mechanics and Spectral Theory" (online), ICMP 2021, August 2-7 2021.
Special Session " Mathematical Methods in Quantum Mechanics" (online), MCA 2021, July 12-23, 2021.
Spectral theory summer conference (online), Nanjing, July 11-13, 2021.
The 38th Western States Meeting (online), Caltech, February 20-21, 2021.
(Cancelled) Workshop "New trends in Lyapunov exponents" July 6-10, 2020, University of Lisbon, Lisbon, Portugal.
(Cancelled) New directions in disordered systems, Cergy, France, June 28 - July 3rd 2020.
(Cancelled) Almost-Periodic Spectral Problems, BIRS workshop, Banff, Canada, April 12-17, 2020.
(Cancelled) 10 Ohio River Analysis Meeting, University of Kentucky, Lexington, Kentucky, March 20-21, 2020.
The 37th Annual Western States Meeting of Mathematical Physics, UC Irvine, California, March 7-8, 2020.
Texas Analysis and Mathematical Physics Symposium 2019/20, Rice University, Houston, TX, January 31-February 2, 2020.
AMS Special Session on Spectral and Transport Properties of Disordered Systems, Joint Mathematics Meetings, Denver, CO, January 15-18, 2020.
AMS Special Session on Dynamical Systems and Ergodic Theory, UC Riverside, CA, November 9-10, 2019.
The 2nd Annual Meeting of the SIAM Texas Louisiana Section，Southern Methodist University, Dallas, TX, November 1-3, 2019.
The Great Lakes Mathematical Physics meeting 2019, Oberlin College, June 28-30, 2019. Webpage
AMS Special Session on Localization and Delocalization for Disordered Quantum Systems, Joint Mathematics Meetings, Baltimo, MD, January 16-19, 2019. Webpage
Spectral Theory of Quasi-Periodic and Random Operators, November 12-16, 2018. Webpage
Anderson localization for high dimensional quasi-periodic operators with long-range interactions (AMS Special Session on Ergodic and Topological Quantum Systems, University of Michigan, October 20-21, 2018). Webpage
The third Great Lakes Mathematical Physics Meeting, June 22-24, 2018. Webpage
Global Young Scholar Forum, Sichuan University, Chengdu, Sichuan, China, May 14-17, 2018. Webpage
Special Session on Spectral Theory, AMS Spring Western Sectional Meeting Portland State University, Portland, OR , April 14-15, 2018. Webpage
Sharp spectral transitions for singular spectrum and growth of eigenfunctions of Laplacians on Riemannian manifolds (The 36th Annual Western States Meeting of Mathematical Physics, UCI, Feb 18-Feb 19, 2018). Webpage
Special Session on Analysis and Geometry of Fractals, AMS Fall Western Sectional Meeting, UC Riverside, Nov 4-5, 2017. Webpage
Sharp spectral transitions and growth of eigenfunctions of Laplacians on Riemannian manifolds (9th St. Petersburg Conference in Spectral Theory dedicated to the memory of M. Sh. Birman, Euler Institute, St. Petersburg, Russia, 3-6 July, 2017). Webpage
Universal Hierarchical Structure of the Almost Mathieu Eigenfunctions (Young Researcher Symposium, Toronto, Canada, Aug 22-Aug 26, 2016). Webpage
Sharp arithmetic spectral transitions and bounds on quantum dynamics for supercritical almost Mathieu operators (Great Lakes Mathematical Physics Meeting 2016, MSU, June 17-June 19, 2016). Webpage
Sharp arithmetic spectral transitions and bounds on quantum dynamics for supercritical almost Mathieu operators (Simons Center's Workshop: Between Dynamics and Spectral Theory, Stony Brook, New York, June 6-June 10, 2016). Webpage
Sharp spectral transitions and exact asymptotics of the eigenfunctions and transfer matrices for the almost Mathieu operator (The 34th Annual Western States Meeting of Mathematical Physics, Caltech, Feb 15-Feb 16, 2016). Webpage
The asymptotics of generalized eigenfunctions of quasiperiodic operators (KAM Workshop, Fudan University, Jan 8, 2016). Webpage
Exact asymptotics of the eigenfunctions and transfer matrices for the almost Mathieu operator (AMS Fall Western Sectional Meeting, California State University, Fullerton, Oct 24-Oct 25, 2015). Webpage
Spectral transitions for quasiperiodic operators (The Sixth Spectral Theory of Ordinary Differential Operator, NJUST, May 22-May 23, 2015). Webpage
Arithmetic Spectral Transitions for the Maryland Model (The workshop "Almost-Periodic and Other Ergodic Problems", Isaac Newton Institute for Mathematical Sciences, Cambridge, Apr 7, 2015). Webpage
Spectral transitions for quasiperiodic operators (Doctorial Forum of Mathematics between Fudan and Kyoto University, Fudan University, Shanghai, Nov 2-Nov 8, 2014). Webpage
The Spectral types of the Maryland Model ( USA-Uzbekistan Conference, California State University, Fullerton, May 19-May 23, 2014). Webpage
Some refined results on almost Mathieu operator in exponential regime (The 32th Annual Western States Meeting of Mathematical Physics, Caltech, Feb 17-Feb 18, 2014). Webpage
Seminar Talks
Analysis Seminar, SUNY at Buffalo, April 10, 2024.
Dynamics and Groups Seminar, Texas A&M University, Feb 14, 2024.
Dynamics and Groups Seminar, Texas A&M University, Feb 7, 2024.
Applied Math Undergraduate Seminar, Texas A&M University, November 15, 2023.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, March 27, 2023.
Math Physics Seminar, Georgia Tech, March 16, 2023.
Differential Equations and Applied Math Seminar, Texas State University, Oct 14, 2022.
Shanghai Polytechnic University, Shanghai, Sep 9, 2022
School of Physics, Henan Normal University, June 27, 2022.
Spectral geometry in the clouds (online), August 23, 2021.
Chongqing Technology and Business University (online), June 20, 2021.
London Analysis Seminar (online), May 13, 2021.
Differential Equations Seminar (online), Michigan University, April 8, 2021.
Differential Equations and Applied Math Seminar (online) , Texas State University, March 26, 2021.
EIMI Seminar on spectral theory and related topics (online), the Euler International Mathematical Institute, March 17, 2021.
Mathematical Physics Seminar (online), UC Irvine, February 11, 2021.
(Cancelled) Analysis Seminar, Baylor University, April 29, 2020.
Mathematical Physics Seminar, UC Irvine, March 12, 2020.
Dynamical Systems Seminar, University of Houston, February 24, 2020.
Linear Analysis Seminar, Texas A&M University, February 7, 2020.
Mathematical Physics Seminar, UC Irvine, November 14, 2019.
Spectral Theory Brown Bag Seminar, Rice University, October 23, 2019.
Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, October 4, 2019.
Anderson localization for quasiperiodic operators and related Hamiltonian PDEs (Ergodic Schrödinger Operator Seminar, UCI, April 15, 2019). Webpage
Anderson localization for quasiperiodic operators and related Hamiltonian PDEs (Ergodic Schrödinger Operator Seminar, UCI, April 8, 2019). Webpage
Spectral transitions for Schrödinger operators with decaying potentials and Laplacians on asymptotically flat (hyperbolic) manifolds (Nonlinear PDE Seminar, UCI, Oct 26, 2018). Webpage
Spectral transitions for Schrödinger operators with decaying potentials and Laplacians on asymptotically flat (hyperbolic) manifolds (Applied Math & Analysis Seminar, Duke University, Oct 2, 2018). Webpage
Sharp spectral transition for the Schrödinger operator and its applications (UESTC, Chengdu, May 17, 2018). Webpage
Singular spectra for quasiperiodic operators in positive Lyapunov exponent regime (Dynamics System Seminar, Sichuan University, May 14, 2018). Webpage
Embedded eigenvalues for the discrete Schrödinger operator (Ergodic Theory and Spectral Theory Seminar, UCR, May 4, 2018). Webpage
Inhomogeneous Diophantine approximation in the coprime setting (Number Theory Seminar, UCI, Nov 16, 2017). Webpage
Sharp spectral transition for eigenvalues embedded into the spectral bands (Mathematical Physics Seminar, UCI, Nov 9, 2017). Webpage
Some refined results on mixed Littlewood conjecture for pseudo-absolute values (Mathematical Physics Seminar, UCI, Aug 3, 2017). Webpage
Universal hierarchical (reflective hierarchical) structure of the almost Mathieu eigenfunctions (Dynamics System Seminar, Sichuan University, June 26, 2017).Webpage
The HRT conjecture for almost every (1,3) configuration (Sichuan University, June 23, 2017). Webpage
The Littlewood conjecture for pseudo-absolute values (Sichuan University, June 22, 2017). Webpage
Sharp spectral transitions and growth of eigenfunctions of Laplacians on Riemannian manifolds (Dynamics System Seminar, Fudan University, June 19, 2017).Webpage
The HRT conjecture for almost every (1,3) configuration (Shanghai Second Polytechnic University, June 18, 2017).
Noncompact manifolds with embedded singular spectra on their Laplacians (NJUST, Nanjing, June 16, 2017). Webpage
Strichartz estimates for endpoint (Ergodic Schrödinger Operator Seminar, UCI, May 1, 2017). Webpage
Strichartz estimates for non-endpoint (Ergodic Schrödinger Operator Seminar, UCI, April 24, 2017). Webpage
Dispersive and Strichartz estimates for free Laplacians (Ergodic Schrödinger Operator Seminar, UCI, April 18, 2017). Webpage
Introduction to limiting absorption principle and its application to spectral theory (Ergodic Schrödinger Operator Seminar, UCI, Feb 3, 2017). Webpage
Growth properties of eigensolutions of Laplacians in higher dimensions (Ergodic Schrödinger Operator Seminar, UCI, Jan 13, 2017). Webpage
Spectral transitions of Laplacians with decaying potentials (Ergodic Schrödinger Operator Seminar, UCI, Jan 6, 2017). Webpage
Arithmetic criteria for quasiperiodic Schrödinger operators (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 21, 2015).
Dry version of the ten Martini problem ((Mathematical Physics Seminar, UCI, Apr 10, 2014). Webpage
Anderson Localization for almost Mathieu operators with Liouville frequencies ((Mathematical Physics Seminar, UCI, Feb 27, 2014). Webpage
Summer Schools and Minicourses
Summer Graduate School: Periodic and Ergodic Spectral Problems, Montreal, Canada, June 19- June 30, 2023.
Green's function estimates for Lattice Schrödinger operators and applications, Dalian University of Technology, July 15-July 22, 2015. Webpage
Spectral theory of quasiperiodic operators, Suzhou University, Dec 24-Dec 27, 2013. Webpage
Conferences attended
Honoring the Life and Work of Jean Bourgain, IAS, May 31-June 1,2019. Webpage
The XIX International Congress on Mathematical Physics, Montreal, Quebec, Canada, July 23 to July 28, 2018. Webpage
Young Researchers Symposium , Montreal, Quebec, Canada, July 20 and 21, 2018. Webpage
PCMI Research Program, Park City, Utah, July 1-19, 2018. Webpage
Classical and Quantum Motion in Disordered Environment: A Random Event in honour of Ilya Goldsheid's 70-th birthday, Queen Mary, University of London, Dec 18 to Dec 22, 2017. Webpage
35th Annual Western States Mathematical Physics Meeting, Caltech, Feb 12-Feb 13, 2017. Webpage
Frontiers in Mathematical Physics on the Occasion of the 70th Birthday of Barry Simon, Montreal, Canada, Aug 28-Sep 1, 2016. Webpage
Analysis and beyond: celebrating Jean Bourgain’s work and its impact, Princeton, May 21- May 24, 2016. Webpage
The Workshop on Hamiltonian dynamical systems, Fudan University, Jan 04-Jan 10, 2015. Webpage