# Abstract for the talk on 05.11.2018 (17:00 h)

**Arbeitsgemeinschaft ANGEWANDTE ANALYSIS**

*Stephen Green*(MPI for Gravitational Physics)

**Nonlinear Frontiers in General Relativity**

General relativity, our modern theory of gravity, connects the matter

content of the universe to spacetime geometry through the Einstein

equation. It endows geometry with rich dynamics: solutions describe

cosmology, black holes, neutron stars and gravitational waves, all of

which came together in the binary merger events detected by LIGO and

Virgo. The nonlinear nature of the Einstein equation gives rise to

these dynamics, but at the same time makes finding solutions a

challenge.

In this talk I will describe two nonlinear frontiers of general

relativity research. At the "dynamical frontier" weakly dissipative

systems give rise to new nonlinear dynamics, including instabilities

and even turbulence in the spacetime geometry. A major finding is the

emergence of new approximate conservation laws that control turbulent

cascades. These systems are often relevant to conjectured holographic

dualities, and may manifest astrophysically. At the "deep learning

frontier" I will describe data challenges facing gravitational-wave

astronomy, and approaches to try to solve them with deep neural

networks.