Education

• September 2012- July 2015 PhD in Mathematics, Fudan  University, China. Thesis: Spectral theory of one-dimensional quasi-periodic Schrodinger operators. Advisor: Xiaoping Yuan

• September 2006-  January 2012   BS and MS in Mathematics, Nanjing University of Science and Technology, China. Thesis: Topics on Liouville operators. Advisor: Zhenyou Huang

Appointments

• 2023- present  Associate professor, Department of Mathematics, Texas A&M University

• 2019- 2023       Assistant Professor, Department of Mathematics, Texas A&M University

• 2015- 2019       Visiting Assistant Professor, Department of Mathematics, UC Irvine. Mentor: Svetlana Jitomirskaya

Honours & Awards

• IUPAP Prize at the ICMP 2024

• Simons Fellow   2024-2025

• Frontiers of Science Award (shared with Svetlana Jitomirskaya) at  the inaugural International Congress of Basic Science, 2023

• Invited Speaker,  XX International Congress of Mathematical Physics (ICMP), Geneva, 2021

Editorial boards

•  Journal of Spectral Theory,  2023-present

Grants

• 2023-2026  NSF DMS-2246031

• 2021-2024  FRG Grant,  NSF DMS-2052572

• 2020-2023  NSF DMS-2000345 

• 2017-2020  NSF DMS-1700314 (transferred to TAMU as DMS-2015683)

• 2016-2018  AMS-Simons Travel Grant

Selected Publications

• 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 

• W. Liu.  Small  denominators and  large numerators of quasiperiodic Schrodinger  operators. Peking Math J to appear.  arXiv version

• W. Liu. Fermi isospectrality for discrete periodic Schrodinger operators. Comm. Pure Appl. Math. 77 (2024), no. 2, 1126–1146. arXiv version

• W. Liu. Distributions of  resonances of  supercritical  quasi-periodic operators.  Int. Math. Res. Not. IMRN 2024, no. 1, 197--233. arXiv version

• S. Jitomirskaya and W. Liu. Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase. J. Eur. Math. Soc. (JEMS) 26 (2024), no. 8, 2797--2836. 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

•  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

• 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

• 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 

•  S. Jitomirskaya and W. Liu. Universal hierarchical structure  of  quasiperiodic eigenfunctions.   Ann. of Math. (2) 187 (2018), no. 3, 721-776. 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

Graduate Students

• Kang Lyu, 2021-present

• Matthew Faust  (joint with F. Sottile, PhD 2024; now postdoc at MSU)

• Matthew Powell  (joint with S. Jitomirskaya, PhD 2023;  now Hale Visiting Assistant Professor at  Georgia Tech)

• Yunfeng Shi (co-supervisor, Ph.D. 2018, Boya Postdoctoral Fellow at  Peking University 2018-2020;  now Associate  Professor at Sichuan University)

 Postdoctoral Scholars

• Xueyin Wang,  2024-present

• Rodrigo Matos  (VAP at TAMU 2020-2023; now Assistant Professor at PUC Rio)