Speaker:  Professor Larry Guth - MIT Mathematics

Title: Focusing waves and combinatorics of lines

Abstract: Solutions of the wave equation model sound waves, light waves, etc.  Focusing refers to the amplitude getting very large in a small region of space.  Estimating how much waves can focus is a problem in real analysis.  Over the last 25 years, mathematicians have approached this problem using ideas from combinatorics about the intersection patterns of lines.  The story involves parts of math that sound rather far from PDE, such as some topology and some finite fields.  In this talk, we will begin with a gentle introduction to waves and the wave equation, and then describe how ideas from some of these other fields come into play.