The phenomenon of wave propagation in random environments appears in many physical situations of practical interest. The simplest model for this phenomenon is the Schrodinger equation coupled to a weak random potential, which describes the evolution of an electron in disordered media. The effect of the disorder is to scatter the wave into random directions. The long-time behavior is described by an effective diffusion equation, which was first established by Erdös, Salmhofer, and Yau using sophisticated diagrammatic arguments. In this talk I will describe a new approach to proving this effective limit which uses a wavepacket decomposition of the solution to give a geometric meaning to the diagrams. I will focus on the geometry of the diagrams and state some elementary open problems concerning Euclidean geometry which suggest a path to simpler proofs and stronger results.

Zoom Room: https://umich.zoom.us/j/96021646996