Oscar Pezzi: Waves, Cones and Oscillations

Abstract: The wave equation is one of the most fundamental models in mathematics and physics, describing how sound, light, or other disturbances move through space and time. In this talk, we will look at the Cauchy problem for the wave equation — how waves evolve from given initial data — and see how oscillatory integrals help us understand their behavior. We will explore how the solution can be expressed using the Fourier transform, and how the geometry of the light cone determines where and how the wave propagates. Along the way, we’ll discuss the surprising difference between even and odd spatial dimensions, known as Huygens’ principle, and see how oscillatory integrals provide a natural language to describe this and other wave phenomena.