Research
My research lies in applied analysis and partial differential equations, with a particular focus on multiscale modelling, electromagnetic wave propagation, and variational methods.
Research areas
I am interested in rigorous mathematical models that connect microscopic structure with effective macroscopic behaviour. My current work is organized around three closely related areas.
Electromagnetic waves
Maxwell equations & wave propagation
Effective interface conditions for thin periodic structures, metasurfaces, polarization-dependent transmission, reflection, and electromagnetic wave propagation.
Multiscale analysis
Homogenization & multiscale media
Rigorous upscaling of PDEs in periodic and evolving microstructures, including porous media, transport processes, fluid flow, memory effects, and moving geometries.
Nonlinear analysis
Calculus of variations
Polyconvexity, isotropic energy densities, nonlinear elasticity, relaxation, dimension reduction, and neural-network-based constitutive models.
Common perspective
Across these topics, a recurring theme is the derivation and analysis of effective equations for systems whose behaviour is determined by geometry or material structure on a smaller scale. The mathematical tools include homogenization, variational methods, functional analysis, compactness arguments, and the analysis of partial differential equations.
Applications
The applications range from electromagnetic metasurfaces and polarization devices to transport and flow in porous media and constitutive models in nonlinear solid mechanics.