Spectral theory is concerned with the mathematical properties of linear operators through the study of their spectra and eigenelements. It has emerged as a key area of mathematics for the precise analysis of both quantum and classical wave phenomena, in the context of acoustic, electromagnetic or mechanical wave propagation. It is therefore a key mathematical tool in the understanding of many physical phenomena.

In both classical and quantum physics, the engineering development of materials with increasingly complex physical properties (e.g. metamaterials, topological insulators, etc.) or geometrical properties (e.g. waveguides or curved optical fibers) raises important new questions in this area of mathematics, in order to model wave propagation in such media. What’s more, these “new materials” have numerous application challenges.

This workshop is organized within the framework of the AMIDEX project Propagation in Twisted Waveguides (PTW) and follows the thematic day Spectral Theory Applied to Physics, held at CIRM in October 2024. While the first edition had a primarily local scope within Aix-Marseille University (CPT, I2M, Institut Fresnel, and LMA), this new edition also opens to a national and international dimension. It also follows the five-day international conference “Wave Propagation in Guiding Structures”, organized by members of the project in October 2025, which brought together more than 80 participants from 15 countries. Thus, the aim of this new event is to revive and stimulate discussions and collaborations in these research areas, which are essential in physics and engineering, particularly as the PTW project is administratively scheduled to conclude at the end of 2026. Furthermore, a half-day will be devoted to the spectral study of graphene models within the framework of the CNRS IRP SPEDO project.