|Date: Tuesday, January 23, 2018
Title: The Mathematics of Gravitational Waves.
Abstract: In mathematical general relativity the Einstein equations describe the laws of the universe, giving the latter a geometric structure. This system of hyperbolic nonlinear partial differential equations (pde) has served as a playground for all kinds of new methods and results in pde analysis, geometry and other fields. A main goal in the study of these equations is to investigate the analytic and geometric properties of the solution spacetimes. Some of the most interesting solutions of the Einstein equations are spacetimes exhibiting gravitational radiation. A major breakthrough of general relativity happened in 2015 with LIGO's first detection of gravitational waves from black hole mergers. This marks the beginning of a new era, where these waves tell us about mathematical and physical properties of their sources. In this talk, I will first lay out some basics of mathematical general relativity, then we will delve into the mathematical description of gravitational radiation. Along the way, I will briefly highlight the Cauchy problem and the dynamics of black holes. Finally, I will explain some of our new results on how gravitational waves permanently change the spacetime.
Speaker: Lydia Bieri
Institution: University of Michigan