HR job title
- Associate Professor
- Contact Info
- Websites
- ORCiD
- 0000-0001-5154-6474
Liu, Wencai Associate Professor
Positions
- associate professor, Mathematics, College of Arts and Sciences
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Overview
Publications
selected publications
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academic article
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Faust, M., Liu, W., Matos, R., Plute, J., Robinson, J., Tao, Y., Tran, E., & Zhuang, C.
(2024).
Floquet isospectrality of the zero potential for discrete periodic Schrdinger operators. Journal of Mathematical Physics.
65(7), 073501.
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Fillman, J., Liu, W., & Matos, R.
(2024).
Algebraic properties of the Fermi variety for periodic graph operators. Journal of Functional Analysis.
286(4), 110286-110286.
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Liu, W.
(2024).
Fermi isospectrality for discrete periodic Schrdinger operators. Communications on Pure and Applied Mathematics.
77(2), 1126-1146.
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Kachkovskiy, I., Liu, W., & Wang, W.
(2024).
Spacetime quasiperiodic solutions to a nonlinear Schrodinger equation on Z. Journal of Mathematical Physics.
65(1), 011502.
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Liu, W.
(2023).
Floquet isospectrality for periodic graph operators. 374, 642-653.
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Jitomirskaya, S., & Liu, W.
(2023).
Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase. Journal of the European Mathematical Society (Print).
26(8), 2797-2836.
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Liu, W.
(2023).
Fermi Isospectrality of Discrete Periodic Schrodinger Operators with Separable Potentials on Z2. 399(2), 1139-1149.
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Liu, W.
(2023).
Power law logarithmic bounds of moments for long range operators in arbitrary dimension. Journal of Mathematical Physics.
64(3), 033508.
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Liu, W.
(2023).
Distributions of Resonances of Supercritical Quasi-Periodic Operators. International mathematics research notices.
2024(1), 197-233.
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Fillman, J., Liu, W., & Matos, R.
(2022).
Irreducibility of the Bloch variety for finite-range Schrodinger operators. 283(10), 109670-109670.
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Liu, W.
(2022).
IRREDUCIBILITY OF THE FERMI VARIETY FOR DISCRETE PERIODIC SCHRODINGER OPERATORS AND EMBEDDED EIGENVALUES. 32(1), 1-30.
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Liu, W.
(2022).
Topics on Fermi varieties of discrete periodic Schrodinger operators. 63(2), 023503.
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Liu, W.
(2022).
QUANTITATIVE INDUCTIVE ESTIMATES FOR GREEN'S FUNCTIONS OF NON-SELF-ADJOINT MATRICES. Analysis and PDE.
15(8), 2061-2108.
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Liu, W.
(2021).
Criteria for Embedded Eigenvalues for Discrete Schrodinger Operators. International mathematics research notices.
2021(20), 15803-15832.
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Jitomirskaya, S., & Liu, W.
(2021).
Upper bounds on transport exponents for long-range operators. Journal of Mathematical Physics.
62(7), 073506.
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Liu, W.
(2021).
Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrodinger operators. 34(3), 1288-1315.
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Liu, W., & Ong, D. C.
(2020).
SHARP SPECTRAL TRANSITION FOR EIGENVALUES EMBEDDED INTO THE SPECTRAL BANDS OF PERTURBED PERIODIC OPERATORS. Journal d'Analyse Mathematique.
141(2), 625-661.
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Liu, W.
(2020).
Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators. 293(9), 1776-1790.
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Jitomirskaya, S., & Liu, W.
(2020).
NONCOMPACT COMPLETE RIEMANNIAN MANIFOLDS WITH SINGULAR CONTINUOUS SPECTRUM EMBEDDED INTO THE ESSENTIAL SPECTRUM OF THE LAPLACIAN, I. THE HYPERBOLIC CASE. Transactions of the American Mathematical Society.
373(8), 5885-5902.
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Liu, W.
(2020).
Almost Mathieu operators with completely resonant phases. Ergodic Theory and Dynamical Systems.
40(7), 1875-1893.
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Liu, W.
(2020).
Growth of the Eigensolutions of Laplacians on Riemannian Manifolds I: Construction of Energy Function. International mathematics research notices.
2020(9), 2561-2587.
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Liu, W.
(2020).
The Mobius transformation of continued fractions with bounded upper and lower partial quotients. Turkish Journal of Mathematics.
44(3), 813-824.
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Jitomirskaya, S., Liu, W., & Shi, Y.
(2020).
Anderson localization for multi-frequency quasi-periodic operators on ZD. 30(2), 457-481.
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Jitomirskaya, S., Kruger, H., & Liu, W.
(2020).
Exact dynamical decay rate for the almost Mathieu operator. Mathematical Research Letters.
27(3), 789-808.
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Jitomirskaya, S., & Liu, W.
(2019).
Inhomogeneous Diophantine approximation in the coprime setting. Advances in Mathematics.
355, 106773-106773.
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Liu, W., & Shi, Y.
(2019).
Upper bounds on the spectral gaps of quasi-periodic Schrodinger operators with Lionville frequencies. Journal of Spectral Theory.
9(4), 1223-1248.
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Liu, W.
(2019).
Letter to the Editor: Proof of the HRT Conjecture for Almost Every (1,3) Configuration. Journal of Fourier Analysis and Applications.
25(4), 1350-1360.
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Liu, W.
(2019).
SOME REFINED RESULTS ON THE MIXED LITTLEWOOD CONJECTURE FOR PSEUDO-ABSOLUTE VALUES. Journal of the Australian Mathematical Society.
107(1), 91-109.
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Liu, W.
(2019).
Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators. Journal of Functional Analysis.
276(9), 2936-2967.
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Liu, W.
(2019).
Absence of singular continuous spectrum for perturbed discrete Schrodinger operators. Journal of Mathematical Analysis and Applications.
472(2), 1420-1429.
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Jitomirskaya, S., & Liu, W.
(2019).
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian. GEOMETRIC AND FUNCTIONAL ANALYSIS.
29(1), 238-257.
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Liu, W.
(2018).
Growth of the Eigensolutions of Laplacians on Riemannian Manifolds II: Positivity of the Initial Energy. 21(3), 18.
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Liu, W.
(2018).
Continuous quasiperiodic Schrodinger operators with Gordon type potentials. Journal of Mathematical Physics.
59(6), 063501.
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Jitomirskaya, S., & Liu, W.
(2018).
Universal hierarchical structure of quasiperiodic eigenfunctions. Annals of Mathematics.
187(3), 721-776.
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Jitomirskaya, S., & Liu, W.
(2017).
Arithmetic Spectral Transitions for the Maryland Model. 70(6), 1025-1051.
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Jitomirskaya, S., & Liu, W.
(2017).
A Lower Bound on the Lyapunov Exponent for the Generalized Harper's Model. Journal of Statistical Physics.
166(3-4), 609-617.
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Liu, W.
(2016).
THE SPECTRA OF THE SURFACE MARYLAND MODEL FOR ALL PHASES. Proceedings of the American Mathematical Society.
144(12), 5035-5047.
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Liu, W., & Yuan, X.
(2015).
Anderson localization for the almost Mathieu operator in the exponential regime. Journal of Spectral Theory.
5(1), 89-112.
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Liu, W., & Yuan, X.
(2015).
Spectral gaps of almost Mathieu operators in the exponential regime. 2(1), 1-51.
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Liu, W., & Yuan, X.
(2015).
Anderson localization for the completely resonant phases. Journal of Functional Analysis.
268(3), 732-747.
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Liu, W., & Yuan, X.
(2015).
Holder continuity of the spectral measures for one-dimensional Schrodinger operator in exponential regime. Journal of Mathematical Physics.
56(1), 012701.
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Liu, W., & Huang, Z.
(2013).
On the Relationship of the Spectra of the Self-adjoint Operator and its Liouville Operator. 52(8), 2578-2591.
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Liu, W., & Huang, Z.
(2013).
The Generalized Eigenvector Expansions of the Liouville Operator. International Journal of Theoretical Physics.
52(12), 4323-4334.
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Liu, W., & Wang, W.
Nonlinear Anderson Localized States at Arbitrary Disorder. Communications in Mathematical Physics.
405(11), 272.
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Liu, W.
Small Denominators and Large Numerators of Quasiperiodic Schrdinger Operators. Peking Mathematical Journal.
1-30.
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Faust, M., Liu, W., Matos, R., Plute, J., Robinson, J., Tao, Y., Tran, E., & Zhuang, C.
(2024).
Floquet isospectrality of the zero potential for discrete periodic Schrdinger operators. Journal of Mathematical Physics.
65(7), 073501.
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chapter
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Liu, W., & Lyu, K.
(2023).
One Dimensional Discrete Schrdinger Operators with Resonant Embedded Eigenvalues. Operator Theory Advances and Applications.
From Complex Analysis to Operator Theory: A Panorama.
(pp. 619-636).
Springer Nature.
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Jitomirskaya, S., Liu, W., & Zhang, S.
(2020).
Arithmetic spectral transitions: A competition between hyperbolicity and the arithmetics of small denominators. Harmonic Analysis and Applications.
(pp. 35-72).
American Mathematical Society (AMS).
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Liu, W., & Lyu, K.
(2023).
One Dimensional Discrete Schrdinger Operators with Resonant Embedded Eigenvalues. Operator Theory Advances and Applications.
From Complex Analysis to Operator Theory: A Panorama.
(pp. 619-636).
Springer Nature.
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institutional repository document
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Faust, M., Liu, W., Matos, R., Plute, J., Robinson, J., Tao, Y., Tran, E., & Zhuang, C.
(2024).
Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrdinger Operators
-
Liu, W.
(2023).
Proof of geometric Borg's Theorem in arbitrary dimensions
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Fillman, J., Liu, W., & Matos, R.
(2023).
Algebraic Properties of the Fermi Variety for Periodic Graph Operators
-
Liu, W.
(2023).
Floquet isospectrality for periodic graph operators
-
Liu, W.
(2022).
Power law logarithmic bounds of moments for long range operators in arbitrary dimension
-
Liu, W.
(2022).
Bloch varieties and quantum ergodicity for periodic graph operators
-
Liu, W.
(2022).
Distributions of resonances of supercritical quasi-periodic operators
-
Liu, W.
(2022).
Fermi isospectrality of discrete periodic Schrdinger operators with separable potentials on $mathbb{Z}^2$
-
Liu, W., & Lyu, K.
(2022).
One dimensional discrete Schrdinger operators with resonant embedded eigenvalues
-
Liu, W.
(2022).
Small denominators and large numerators of quasiperiodic Schrdinger operators
-
Liu, W., & Wang, W.
(2022).
Nonlinear Anderson localized states at arbitrary disorder
-
Liu, W.
(2021).
Topics on Fermi varieties of discrete periodic Schrdinger operators
-
Fillman, J., Liu, W., & Matos, R.
(2021).
Irreducibility of the Bloch Variety for Finite-Range Schrdinger Operators
-
Liu, W.
(2021).
Fermi isospectrality for discrete periodic Schrodinger operators
-
Jitomirskaya, S., & Liu, W.
(2021).
Upper bounds on transport exponents for long range operators
-
Liu, W.
(2020).
Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
-
Liu, W.
(2020).
Revisiting the Christ-Kiselev's multi-linear operator technique and its applications to Schrdinger operators
-
Liu, W.
(2020).
Irreducibility of the Fermi variety for discrete periodic Schrdinger operators and embedded eigenvalues
-
Jitomirskaya, S., Liu, W., & Shi, Y.
(2019).
Anderson localization for multi-frequency quasi-periodic operators on $mathbb{Z}^d$
-
Jitomirskaya, S., & Liu, W.
(2019).
Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
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Jitomirskaya, S., Krger, H., & Liu, W.
(2018).
Exact dynamical decay rate for the almost Mathieu operator
-
Liu, W.
(2018).
Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
-
Liu, W.
(2018).
Absence of singular continuous spectrum for perturbed discrete Schrdinger operators
-
Liu, W.
(2018).
Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
-
Liu, W.
(2018).
The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators
-
Liu, W.
(2018).
Criteria for embedded eigenvalues for discrete Schrdinger operators
-
Liu, W.
(2018).
Almost Mathieu operators with completely resonant phases
-
Liu, W., & Ong, D. C.
(2018).
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
-
Liu, W., & Ong, D. C.
(2018).
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
-
Jitomirskaya, S., & Liu, W.
(2018).
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
-
Jitomirskaya, S., & Liu, W.
(2018).
Inhomogeneous Diophantine approximation in the coprime setting
-
Jitomirskaya, S., & Liu, W.
(2018).
Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase
-
Liu, W.
(2017).
Continuous quasiperiodic Schrdinger operators with Gordon type potentials
-
Liu, W.
(2017).
Sharp bound on the largest positive eigenvalue for one-dimensional Schrdinger operators
-
Liu, W.
(2017).
Some refined results on mixed Littlewood conjecture for pseudo-absolute values
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Liu, W.
(2017).
Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function
-
Liu, W.
(2017).
Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy
-
Liu, W., & Shi, Y.
(2017).
Upper bounds on the spectral gaps of quasi-periodic Schrdinger operators with Liouville frequencies
-
Jitomirskaya, S., & Liu, W.
(2016).
A lower bound on the Lyapunov exponent for the generalized Harper's model
-
Jitomirskaya, S., & Liu, W.
(2016).
Arithmetic Spectral Transitions for the Maryland Model
-
Liu, W.
(2016).
The spectra of surface Maryland model for all phases
-
Jitomirskaya, S., & Liu, W.
(2016).
Universal hierarchical structure of quasiperiodic eigenfunctions
-
Liu, W.
(2016).
Proof of the HRT conjecture for almost every (1,3) configuration
-
Liu, W.
(2016).
The Mbius transformation of continued fractions with bounded upper and lower partial quotients
-
Liu, W., & Yuan, X.
(2013).
Absolutely Continuous Spectrum for the Quasi-periodic Schrdinger Operator in Exponential Regime
-
Liu, W., & Yuan, X.
(2013).
Anderson localization for the completely resonant phases
-
Liu, W., & Yuan, X.
(2013).
Hlder Continuity of the Spectral Measures for One-Dimensional Schrdinger Operator in Exponential Regime
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Liu, W., & Yuan, X.
(2013).
Spectral Gaps of Almost Mathieu Operator in Exponential Regime
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Liu, W., & Yuan, X.
(2013).
Anderson Localization for the Almost Mathieu Operator in Exponential Regime
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Liu, W., Powell, M., & Wang, X.
Quantum dynamical bounds for long-range operators with skew-shift potentials
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Liu, W., Matos, R., & Treuer, J. N.
Sharp decay rate for eigenfunctions of perturbed periodic Schrdinger operators
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Jitomirskaya, S., Liu, W., & Mi, L.
Sharp palindromic criterion for semi-uniform dynamical localization
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Faust, M., Liu, W., Matos, R., Plute, J., Robinson, J., Tao, Y., Tran, E., & Zhuang, C.
(2024).
Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrdinger Operators
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thesis
Research
principal investigator on
- (Semi)Algebraic Geometry In Schrodinger Operators And Nonlinear Hamiltonian Partial Differential Equations awarded by National Science Foundation - (Arlington, Virginia, United States) 2023 - 2026
- Hamiltonian Systems and Related Phenomena awarded by Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States) 2020 - 2023
- Problems in Spectral Theory and Analysis awarded by Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States) 2019 - 2020
- FRG: Collaborative Research: Non-perturbative analysis of multi-dimensional quasiperiodic problems awarded by National Science Foundation - (Arlington, Virginia, United States)
Teaching
teaching activities
- MATH171 Calculus I Instructor
- MATH304 Linear Algebra Instructor
- MATH308 Differential Equations Instructor
- MATH491 Hnr-research Instructor
- MATH491 Research Instructor
- MATH663 Seminar In Analysis Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
Background
education and training
- Ph.D. in Mathematics, Fudan University - (Shanghai, Shanghai, China) 2015
awards and honors
- Fellows in Mathematics, conferred by Simons Foundation - (New York, New York, United States), 2024
Contact
first name
- Wencai
has last name
- Liu
Other
- wencail@tamu.edu