Résumé : In 1981, W.G. Unruh discovered a mathematical analogy between waves in condensed matter systems and massless scalar fields in a curved space-time. This discovery founded the field of analogue gravity and offered the possibility to experimentally access fundamental effects otherwise out of reach, such as Hawking radiation, superradiance, or cosmological particle production. The observation of these effects in analogue gravity experiments has stimulated the development of mathematical models required to describe these experiments and resulted in a better understanding for the fundamental processes at play. In this talk, I will give an overview of the field of analogue gravity and its evolution since the 80’s. In particular, I will illustrate the ideas of the field via the examples of analogue superradiance and quasinormal modes emissions. I will then present recent developments and new directions that I am taking in the analogue gravity research program. These include catastrophe theory, uniform asymptotic and resonances of the non-linear Schrödinger equation. I will argue that analogue gravity represents an important tool to better understand fundamental effects in gravitational and condensed matter physics alike, and that it provides fertile grounds for the development and generalisation of mathematical ideas.

connexion: https://teams.microsoft.com/l/meetup-join/19%3ae0d8264434a94a2e93fc6ae0fea08c92%40thread.tacv2/1647020781166?context=%7b%22Tid%22%3a%222fa58faf-7eb1-48b9-9964-a92659d1c5b8%22%2c%22Oid%22%3a%22cac978ae-4f05-466e-9520-2df38186dacf%22%7d
https://indico.math.cnrs.fr/event/7595/