Associate Professor

Biography

Prof. Zhang is an Assistant Professor at HKUST. Before the current position, he was a postdoc at DMA, ENS, Paris.

Research Interests

Applied Math, Inverse Problems, Wave Propagation, Imaging, Super-resolution.

Teaching

• MATH2033  Mathematical Analysis

Awards & Honors

• Professor Hai ZHANG was awarded the 2025 Hong Kong Mathematical Society Young Scholar Award   (2025)
  

Selected Publications

  Article

1. Mathematical theory for the interface mode in an acoustic waveguide bifurcated from a Dirac point
   • Author(s): Qiu, Jiayu; Lin, Junshan; Xie, Peng; Zhang, Hai
   • Source: Communications in Mathematical Sciences, v. 24, (3), p. 749-796
   • Year: 2026


2. Resonances through subwavelength holes: Theory, computation, and applications
   • Author(s): Lin, Junshan; Zhang, Hai
   • Source: Physics Reports, v. 1170, p. 1-34
   • Year: 2026


3. SCAN-MUSIC: an efficient super-resolution algorithm for single snapshot wide-band line spectral estimation
   • Author(s): ZHANG, Hai; FEI, Zetao
   • Source: Numerical Algorithms
   • Year: 2025


4. SCAN-MUSIC: An efficient super-resolution algorithm for large-scale single snapshot line spectral estimation
   • Author(s): Fei, Zetao; Zhang, Hai
   • Source: Numerical Algorithms
   • Year: 2025


5. A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen
   • Author(s): Liang, Ying; Zhang, Hai
   • Source: Journal of Mathematical Physics, v. 65, (7), July 2024, article number 072902
   • Year: 2024


6. IFF: A Superresolution Algorithm for Multiple Measurements
   • Author(s): Fei, Zetao; Zhang, Hai
   • Source: SIAM Journal on Imaging Sciences, v. 16, (4), December 2023, p. 2175-2201
   • Year: 2023


7. Dirac Points for the Honeycomb Lattice with Impenetrable Obstacles
   • Author(s): Li, Wei; Lin, Junshan; Zhang, Hai
   • Source: SIAM Journal on Applied Mathematics, v. 83, (4), August 2023, p. 1546-1571
   • Year: 2023


8. Mathematical Theory for Electromagnetic Scattering Resonances and Field Enhancement in a Subwavelength Annular Gap
   • Author(s): Junshan, Lin; Wangtao, Lu; Zhang, Hai
   • Source: Multiscale Modeling and Simulation, v. 21, (3), September 2023, p. 1012-1052
   • Year: 2023


9. Bulk-interface correspondences for one-dimensional topological materials with inversion symmetry
   • Author(s): Thiang, Guo Chuan; Zhang, Hai
   • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 479, (2270), February 2023, article number 20220675
   • Year: 2023


10. A mathematical theory of the computational resolution limit in one dimension
    • Author(s): Liu, Ping; Zhang, Hai
    • Source: Applied and Computational Harmonic Analysis, v. 56, January 2022, p. 402-446
    • Year: 2022


11. Mathematical theory for topological photonic materials in one dimension
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Journal of Physics A: Mathematical and Theoretical, v. 55, (49), December 2022, article number 495203
    • Year: 2022


12. Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures
    • Author(s): Lin, Junshan; Oh, Sang-Hyun; Zhang, Hai
    • Source: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 86, (1), February 2021, p. 146-164
    • Year: 2021


13. A mathematical theory of computational resolution limit in multi-dimensional spaces
    • Author(s): Liu, Ping; Zhang, Hai
    • Source: Inverse Problems, v. 37, (10), October 2021, article number 104001
    • Year: 2021


14. A Theory of Computational Resolution Limit for Line Spectral Estimation
    • Author(s): Liu, Ping; Zhang, Hai
    • Source: IEEE Transactions on Information Theory, v. 67, (7), July 2021, p. 4812-4827
    • Year: 2021


15. A Mathematical theory for fano resonance in a periodic array of narrow slits
    • Author(s): Lin, Junshan; Shipman, Stephen P.; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 80, (5), September 2020, p. 2045-2070
    • Year: 2020


16. Superresolution Imaging via Subwavelength Hole Resonances
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Physical Review Applied, v. 14, (3), 3 September 2020, article number 034066
    • Year: 2020


17. Fano resonance in metallic grating via strongly coupled subwavelength resonators
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: European Journal of Applied Mathematics, v. 32, (2), 30 June 2020, p. 370-394
    • Year: 2020


18. Photonic Band Gap Phenomenon in a Metal–Dielectric Periodic Structure
    • Author(s): Santosa, Fadil; Zhang, Hai
    • Source: Research in Mathematical Sciences, v. 7, (3), September 2020, article number 15
    • Year: 2020


19. Characterization of the Essential Spectrum of the Neumann-poincaré Operator in 2D Domains With Corner via Weyl Sequences
    • Author(s): Bonnetier, Eric; Zhang, Hai
    • Source: Revista Matematica Iberoamericana, v. 35, (3), 2019, p. 925-948
    • Year: 2019


20. The plasmonic resonances of a bowtie antenna
    • Author(s): Bonnetier, Eric; Triki, Faouzi; Dapogny, Charles; Zhang, Hai
    • Source: Analysis in Theory and Applications, v. 35, (1), April 2019, p. 85-116
    • Year: 2019


21. An Integral Equation Method for Numerical Computation of Scattering Resonances in a Narrow Metallic Slit
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Journal of Computational Physics, v. 385, May 2019, p. 75-105
    • Year: 2019


22. Double-negative acoustic metamaterials
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Lee, Hyundae; Yu, Sanghyeon; Zhang, Hai
    • Source: Quarterly of Applied Mathematics, v. 77, (4), December 2019, p. 767-791
    • Year: 2019


23. Bloch Waves in Bubbly Crystal Near the First Band Gap: A High-frequency Homogenization Approach
    • Author(s): Ammari, Habib; Lee, Hyundae; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v. 51, (1), January 2019, p. 45-59
    • Year: 2019


24. Mathematical Analysis of Surface Plasmon Resonance by a Nano-Gap in the Plasmonic Metal
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v. 51, (6), 2019, p. 4448-4489
    • Year: 2019


25. Shape reconstruction of nanoparticles from their associated plasmonic resonances
    • Author(s): Ammari, Habib; Putinar, Mihai; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal des Mathematiques Pures et Appliquees, v.122, February 2019, p. 23-48
    • Year: 2019


26. Scattering by a Periodic Array of Subwavelength Slits II: Surface Bound States, Total Transmission, and Field Enhancement in Homogenization Regimes
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Multiscale Modeling & Simulation, v. 16, (2), 2018, p. 954-990
    • Year: 2018


27. Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regime
    • Author(s): Zhang, Hai; Lin, Junshan
    • Source: Multiscale Modeling & Simulation, v. 16, (2), May 2018, p. 922-953
    • Year: 2018


28. Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data
    • Author(s): Amman, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Imaging Sciences, v. 11, (1), January 2018, p. 1-23
    • Year: 2018


29. Field Expansions for Systems of Strongly Coupled Plasmonic Nanoparticles
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Numerical Analysis, v. 56, (4), July 2018, p. 2029-2044
    • Year: 2018


30. Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data. Part II: The Strong Interaction Regime
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Imaging Sciences, v. 11, (3), 2018, p. 1931-1953
    • Year: 2018


31. Minnaert Resonances for Acoustic Waves in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, v. 35, (7), November 2018, p. 1975-1998
    • Year: 2018


32. Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
    • Author(s): Ammari, Habib; Millien, Pierre; Ruiz, Matias; Zhang, Hai
    • Source: Archive for Rational Mechanics and Analysis, v. 224, (2), May 2017, p. 597-658
    • Year: 2017


33. Stability for the Lens Rigidity Problem
    • Author(s): Bao, Gang; Zhang, Hai
    • Source: Archive For Rational Mechanics and Analysis, 225, 3, September 2017, p. 1127-1160
    • Year: 2017


34. Scattering and Field Enhancement of a Perfect Conducting Narrow Slit
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 77, (3), 2017, p. 951-976
    • Year: 2017


35. Subwavelength Phononic Bandgap Opening in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Lee, Hyundae; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal of Differential Equations, v. 263, (9), November 2017, p. 5610-5629
    • Year: 2017


36. Sub-wavelength Focusing of Acoustic Waves in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, v.473, (2208), December 2017, article number 20170469
    • Year: 2017


37. A Mathematical and Numerical Framework for Bubble Meta-screens
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 77, (5), October 2017, p. 1827-1850
    • Year: 2017


38. Effective Medium Theory for Acoustic Waves in Bubbly Fluids Near Minnaert Resonant Frequency
    • Author(s): Ammari, Habib; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v.49, (4), August 2017, p. 3252-3276
    • Year: 2017


39. Mathematical and Numerical Framework for Metasurfaces Using Thin Layers of Periodically Distributed Plasmonic Nanoparticles
    • Author(s): Ammari, Habib; Ruiz, Matias; Wu, Wei; Yu, Sanghyeon; Zhang, Hai
    • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 472, (2193), September 2016, article number 20160445
    • Year: 2016


40. Mathematical Analysis of Plasmonic Resonances for Nanoparticles: The Full Maxwell Equations
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal of Differential Equations, v. 261, (6), September 2016, p. 3615-3669
    • Year: 2016


41. Stability analysis for Magnetic Resonance Elastography
    • Author(s): Habib, Ammari; Alden, Waters; Zhang, Hai
    • Source: Journal of Mathematical Analysis and Applications, v. 430, (2), October 2015, p. 919-931
    • Year: 2015


42. Super-resolution in High-contrast Media
    • Author(s): Habib, Ammari; Zhang, Hai
    • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 471, (2178), June 2015, article number 20140946
    • Year: 2015


43. A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators
    • Author(s): Habib, Ammari; Zhang, Hai
    • Source: Communications in Mathematical Physics, v. 337, (1), July 2015, p. 379-428
    • Year: 2015


44. Unique Determination of Periodic Polyhedral Structures by Scattered Electromagnetic Fields II: the Resonance Case
    • Author(s): Gang, Bao; Jun, Zou; Zhang, Hai
    • Source: ransactions of the American Mathematical Society, v. 336, (3), MAR 2014, p. 1333-1361
    • Year: 2014


45. Sensitive Analysis of an Inverse Problem for the Wave Equation with Caustics
    • Author(s): Gang, Bao; Zhang, Hai
    • Source: Journal of the American Mathematical Society, v. 27, (4), October 2014, p. 953-981
    • Year: 2014


46. A Convergent Multiscale Gaussian Beam Parametrix for Wave Equations
    • Author(s): Gang, Bao; Qian, Jianliang; Ying, Lexing; Zhang, Hai
    • Source: Communications in Partial Differential Equations, v. 38, (1), January 2013, p. 92-134
    • Year: 2013


47. Unique determination of periodic polyhedral structures by scattered electromagnetic fields
    • Author(s): Gang, Bao; Zhang, Hai; Jun, Zou
    • Source: Transactions of the American Mathematical Society, v. 363, (9), 2011, p. 4527-4551
    • Year: 2011


48. Recovery of polyhedral obstacles by a single far-field measurement
    • Author(s): Liu, Hongyu; Jun, Zou; Zhang, Hai
    • Source: Journal of Mathematical Physics, v, 50, (12), 2009, p. 123506
    • Year: 2009

  Book

1. Mathematical and Computational Methods in Photonics and Phononics
   • Author(s): Ammari, Habib; Fitzpatrick, Brian; Kang, Hyeonbae; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
   • Year: 2018

  Conference paper

1. Imaging, Multi-Scale and High Contrast PDE
   • Author(s): Zhang, Hai
   • Year: 2014


2. Stability/sensitivity of Recovering Velocity Fields from Boundary Measurements
   • Author(s): Zhang, Hai
   • Year: 2013