Lydia BIERI - The Einstein Equations and  Gravitational Radiation
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2016-06-03

In Mathematical General Relativity (GR) the Einstein equations describe the laws of the  universe.  This  system  of  hyperbolic  nonlinear  pde  has  served as  a  playground for all kinds of new problems and methods in pde analysis and geometry. A major 
goal  in  the  study  of  these  equations  is  to  investigate the  analytic  properties  and geometries of the solution spacetimes. In particular, fluctuations of the curvature of the  spacetime,  known  as  gravitational waves,  have  been  a  highly  active  research 
topic.   A   few   weeks   ago,   it   was confirmed   that   advanced   LIGO   detected gravitational  waves.  Understanding  gravitational  radiation  is  tightly  interwoven  with the study of the Cauchy
problem in GR. I will talk about geometric-analytic results on  gravitational radiation  and  the  memory  effect  of  gravitational  waves.  We  will connect  the mathematical  findings  to experiments.  I  will  also  address  recent  work with
David  Garfinkle  on  gravitational  radiation  in  asymptotically  at  as  well  as cosmological spacetimes.