## Research area

My work is dedicated to the mathematical study of periodic
structures. I particularly focus on the following points:

### Construction and analysis of approximate model for periodic structures

- Asymptotic Analysis (periodic homogenization, asymptotic expansion)
- Maxwell equations, Helmoltz equation
- Numerical simulations

### Simulation of the scattering from periodic gratings using
integral equations

- Development of a robust numerical method valid at and around Wood anomalies
- Periodic Green function
- Integral equations

### Mathematical and numerical investigation of periodic waveguides

- Localized and guided modes
- periodic graphs
- Spectral theory