My research focuses on the development and application of mathematical, computational, and optimization techniques to solve challenging problems in science and engineering. My primary interests include optimization, nonlinear systems of equations, and topological photonics, with an emphasis on numerical methods, scientific computing, and mathematical modeling.
Through my research, I seek to develop efficient computational methods that advance both theoretical understanding and practical applications in applied mathematics, photonics, and engineering.
Research Areas
• Optimization
• Numerical Analysis
• Nonlinear Systems of Equations
• Topological Photonics
• Scientific Computing
• Finite Element Methods
• Finite Difference Methods
• Mathematical Modeling
Current Research Highlights
• Shared spectral band-gap optimization of topological photonic crystals
• Semidefinite programming for photonic crystal design
• Finite element and numerical methods for scientific computing
• Development of Broyden-like methods for large-scale nonlinear systems