PhD in Mathematics
Michigan State University, 2013
Bulk-interface correspondences for one-dimensional topological materials with inversion symmetry
Article
A mathematical theory of the computational resolution limit in one dimension
Article
Mathematical theory for topological photonic materials in one dimension
Article
A mathematical theory of computational resolution limit in multi-dimensional spaces
Article
A Theory of Computational Resolution Limit for Line Spectral Estimation
Article
Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures
Article
A Mathematical theory for fano resonance in a periodic array of narrow slits
Article
Fano resonance in metallic grating via strongly coupled subwavelength resonators
Article
Photonic Band Gap Phenomenon in a Metal–Dielectric Periodic Structure
Article
Superresolution Imaging via Subwavelength Hole Resonances
Article
Article
Bloch Waves in Bubbly Crystal Near the First Band Gap: A High-frequency Homogenization Approach
Article
Article
Double-negative acoustic metamaterials
Article
Mathematical Analysis of Surface Plasmon Resonance by a Nano-Gap in the Plasmonic Metal
Article
Shape reconstruction of nanoparticles from their associated plasmonic resonances
Article
The plasmonic resonances of a bowtie antenna
Article
Field Expansions for Systems of Strongly Coupled Plasmonic Nanoparticles
Article
Minnaert Resonances for Acoustic Waves in Bubbly Media
Article
Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data
Article
Article
Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regime
Article
Article
Mathematical and Computational Methods in Photonics and Phononics
Book
A Mathematical and Numerical Framework for Bubble Meta-screens
Article
Effective Medium Theory for Acoustic Waves in Bubbly Fluids Near Minnaert Resonant Frequency
Article
Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
Article
Scattering and Field Enhancement of a Perfect Conducting Narrow Slit
Article
Stability for the Lens Rigidity Problem
Article
Sub-wavelength Focusing of Acoustic Waves in Bubbly Media
Article
Subwavelength Phononic Bandgap Opening in Bubbly Media
Article
Mathematical Analysis of Plasmonic Resonances for Nanoparticles: The Full Maxwell Equations
Article
Article
A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators
Article
Stability analysis for Magnetic Resonance Elastography
Article
Super-resolution in High-contrast Media
Article
Sensitive Analysis of an Inverse Problem for the Wave Equation with Caustics
Article
Article
Imaging, Multi-Scale and High Contrast PDE
Conference paper
A Convergent Multiscale Gaussian Beam Parametrix for Wave Equations
Article
Stability/sensitivity of Recovering Velocity Fields from Boundary Measurements
Conference paper
A Mathematical and Numerical Framework for Bubble Meta-screens
Effective Medium Theory for Acoustic Waves in Bubbly Fluids Near Minnaert Resonant Frequency
Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
Scattering and Field Enhancement of a Perfect Conducting Narrow Slit
A Mathematical and Numerical Framework for Bubble Meta-screens
Article
Effective Medium Theory for Acoustic Waves in Bubbly Fluids Near Minnaert Resonant Frequency
Article
Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
Article
Scattering and Field Enhancement of a Perfect Conducting Narrow Slit
Article
Stability for the Lens Rigidity Problem
Article
Sub-wavelength Focusing of Acoustic Waves in Bubbly Media
Article
Subwavelength Phononic Bandgap Opening in Bubbly Media
Article
Mathematical Analysis of Plasmonic Resonances for Nanoparticles: The Full Maxwell Equations
Article
Article
A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators
Article
Stability analysis for Magnetic Resonance Elastography
Article
Super-resolution in High-contrast Media
Article
Sensitive Analysis of an Inverse Problem for the Wave Equation with Caustics
Article
Article
Imaging, Multi-Scale and High Contrast PDE
Conference paper
A Convergent Multiscale Gaussian Beam Parametrix for Wave Equations
Article
Stability/sensitivity of Recovering Velocity Fields from Boundary Measurements
Conference paper
MATH5285 | Applied Analysis |
MATH6911D | Reading Course: Scattering Theory in Period Media |
MATH6911D | Reading Course: Scattering Theory in Period Media |
MATH3033 | Real Analysis |
MATH4999 | Independent Capstone Project |
MATH6914J | Reading Course: Spectral Theory of Differential Operators |
MATH2033 | Mathematical Analysis |
MATH5285 | Applied Analysis |
MATH6914J | Reading Course: Spectral Theory of Differential Operators |
No Teaching Assignments |
No Teaching Assignments |
LIU, Xinyu
Mathematics
ZHANG, Jinyang
(co-supervision)
Mathematics
QIU, Jiayu
Mathematics
FEI, Zetao
Mathematics
ZOU, Huaiyang
(co-supervision)
Mathematics
LIU, Ping
Mathematics( Completed in 2021 )
QIU, Jiayu
Mathematics( Completed in 2022 )
FEI, Zetao
Mathematics( Completed in 2021 )
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