Talk Abstract: 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.

Bio: Lydia Bieri is a mathematician working in general relativity and geometric analysis. She earned her doctorate in mathematics from ETH Zurich in 2007 under the supervision of Demetrios Christodoulou. After serving as a Benjamin Peirce Lecturer at Harvard University, she joined the University of Michigan, where she is currently Professor of Mathematics. Her research interests are largely concerned with the mathematical analysis of Einstein's equations, including the study of gravitational radiation, the nonlinear stability and dynamics of spacetime, and the analysis of hyperbolic partial differential equations arising in general relativity, with particular emphasis on asymptotic behaviour and gravitational wave memory effects.