An invitation to cosmological correlators and differential equations

I will give a general and gentle introduction to cosmological correlation functions — their usage as a tool to understand the beginning of the universe, and their connection to particle physics and scattering amplitudes. Then I will show in a toy model of cosmology a beautiful mathematical structure of differential equations that control the strength of the correlations as a function of distances in the sky. In this setup, time evolution emerges as a solution to these static differential equations.