PIMS Network Wide Colloquium: Gigliola Staffilani

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.

Speaker Bio:

Gigliola Staffilani is the Abby Rockefeller Mauze Professor of Mathematics at the Massachusetts Institute of Technology (MIT), where her research focuses on partial differential equations and harmonic analysis, with particular emphasis on dispersive equations and wave turbulence. She serves on the editorial boards of several leading mathematics journals, including the Duke Mathematical Journal and the Journal of the American Mathematical Society, and has received sustained support from the National Science Foundation, the Simons Foundation, and the John Simon Guggenheim Memorial Foundation. A dedicated advocate for women in mathematics, she is a co-organizer of two satellite conferences at International Congress of Mathematicians 2026 and a longtime contributor to the MIT Women in Mathematics program.