The Study of Wave Turbulence: A Meeting Ground for Mathematical Techniques (PIMS network-wide colloquium)

Wave turbulence theory is a rich and expansive field, aiming to provide a framework for understanding how waves interact across different settings. Wave interactions occur over a wide range of scales and media—spanning from gravitational waves in the cosmos to ripples on the ocean’s surface, from the swirling patterns in a morning cup of coffee to quantum particles behaving as wave packets. Despite their ubiquity, these phenomena pose significant challenges to rigorous mathematical analysis. Yet, it is precisely this difficulty that has inspired mathematicians to develop powerful and elegant interdisciplinary methods. In this talk  I will explore some of these approaches, highlighting both the remarkable progress achieved and the intriguing open questions that continue to drive research in this area.