March 29 Math Colloquium

Lydia Bieri, University of Michigan

Spacetime Dynamics

Spacetime geometries arising from the Einstein equations in General Relativity (GR) exhibit all kinds of interesting dynamics. It is gravitation that 'curves' the world. The laws of the Universe, namely Einstein's equations, are geometric-analytic. New insights from geometry and analysis open up new doors in physics. These laws can be written as a system of second order hyperbolic nonlinear partial differential equations. We aim at solving these equations for physical data and explore the classes of solutions with interesting properties. How does a galaxy evolve? What types of initial data create singularities? Are black holes the only singularities in GR? How does the Universe itself evolve? These are important questions that launched a wealth of research and new insights in geometric analysis. In this talk we will explain some of the new mathematical techniques to tackle those problems. We will also connect these to gravitational waves. These waves were observed for the first time in 2015 by the LIGO team (and many times since then). They are also a rich source for new mathematical challenges.

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