Mathematical Physics and Harmonic Analysis Seminar

Date: November 6, 2020

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Mengxuan Yang, Northwestern

Title: Wave Diffraction on Cones and The Aharonov-Bohm Effect

Abstract: Hormander's classic theorem shows the singularities of solutions to the wave equation propagate along the geodesic flow. This is generalized by Cheeger-Taylor and Melrose-Wunsch to manifolds with conic singularities, where the singularities propagate along the so-called diffractive geodesics. In this talk, we will discuss the finer structure of the diffractive wave on cones as well as propagation of singularities for the wave equation with a singular magnetic Laplacian. This latter equation, closely analogous to wave equations with conic singularities, is the setting of the celebrated Aharonov-Bohm effect.