Title: The Einstein Equations and Gravitational Waves
Speaker: Lydia Bieri (University of Michigan)
Abstract: 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. In 2015, gravitational waves were observed for the first time by Advanced LIGO (and several times since then). These waves are produced during the mergers of black holes or neutron stars and in core-collapse supernovae. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will talk about the Cauchy problem for the Einstein equations, explain geometric-analytic results on gravitational radiation and the memory effect of gravitational waves, the latter being a permanent change of the spacetime. We will connect the mathematical findings to experiments.
Biosketch: Lydia Bieri earned her PhD at ETH Zürich in 2007 with Demetrios Christodoulou. She was a Benjamin Peirce Lecturer at Harvard until 2010, before joining the University of Michigan where she is presently. She has coauthored two books: Extensions of the Stability Theorem of the Minkowski Space in General Relativity, a monograph, and Discovering the Expanding Universe, which combines history with mathematical exposition.
Colloquium URL: https://web.math.osu.edu/colloquium/
