Mathematical Theories for Metamaterials

This book develops a rigorous mathematical theory of subwavelength physics derived from first principles, providing a unified framework for the analysis of phenomena arising in metamaterials. It demonstrates the challenges, excitement, and opportunities for research at the interface of mathematics and wave physics. Based on the 2024 NSF-CBMS conference Mathematical Methods for Novel Metamaterials, held at Auburn University, the volume expands on the first author's CBMS lecture series on the mathematical foundations of subwavelength physics. It is written for graduate students and researchers in mathematics interested in condensed matter theory, wave physics, metamaterials, topological materials, and scattering resonances. The exposition is self-contained and assumes only a standard background in partial differential equations.