The purpose of this course is to provide an introduction to well known techniques and to introduce more advanced, state-of-the-art techniques, able to tackle the challenges of the metamaterials by providing a mathematical framework able to explain the observed extraordinary properties of meta-structures and useful to help optimize these properties. These include transformation optics/ transformation elastodynamics, classical and modern homo-genization methodologies, asymptotic and spectral analysis, variational methods, layer potential techniques, as well as modern multi-mathematics. Particular attention will be paid to present practical applications that illustrate the workings and effectiveness of the introduced techniques and discussions on the breakthroughs and the remaining open questions on topical issues in acoustics, electromagnetism, elasticity and in the context of water waves. Bearing these objectives in mind, academic experimental studies as well as commercial devices will be presented during the course.

Applicants must apply at least one month before the beginning of the course.