Analysis & Applied Math

 This is a featured talk

The universe communicates through gravitational waves. In addition to the discrete gravitational wave bursts and their memories (permanent changes of the spacetime), that are encoding information of their sources and the spacetime regions they traversed, the universe is permeated by a stochastic gravitational wave background. By analyzing the Cauchy problem for the Einstein equations in various physical settings, we extract information on the structures of gravitational radiation. At the core of these methods, we make use of the deep interaction of analysis and geometry in the Einstein equations. We shall discuss new results for asymptotically-flat spacetimes as well as for cosmological settings. An overarching challenge involves extracting specific signatures from the highly complex wave fields. We shall also show an example where memory analogues induce interesting questions outside general relativity.

Talk jointly sponsored by the Fields Colloquium in Applied Mathematics.