The upcoming mega-telescopes, such as European Space Agency’s recently launched Euclid satellite, and the upcoming radio Square Kilometer Array (SKA), will provide images of our universe over 10 billion years of cosmic history, and enable us to study its evolution with unprecedented level of detail. In the framework of simulations-based inference, the big telescopes deliver a throve of high-resolution observations and big computers provide the feature-rich numerical theory prediction.

Primordial non-Gaussianities, though yet unobserved, remain an important observable since they can help differentiate various models of inflation. This necessitates a deep understanding of the various processes that could contribute to these non-Gaussianities, with inflationary magnetogenesis being one of them. Often, the spectrum and the bispectrum of the perturbations produced during inflation are studied under the assumption that the metric perturbations can be neglected and that all the relevant physics resides in the coupling of the inflaton and the gauge fields.

A review of the concept of Complexity as have emerged in studying long time properties of systems including blackholes will be presented. Some emphasis will be made on describing features of a particular form of Complexity, the Krylov Complexity. These include its features when interpolating among various types of systems: free, strongly integrable and chaotic ones. Finally I will present a case where we have shown that the value of the Krylov Complexity, a quantum information concept, is equal to the value of a geodesic in a certain background, a geometric concept.

Recent catalog of Faraday rotation measures (RM) of extragalactic sources together with the synchrotron polarization data from WMAP and Planck provide us with the wealth of information on the Galactic magnetic field (GMF). In this talk, we will present a new model of the regular GMF outside of the thin disk. The model is based on several phenomenological components of the GMF -- the spiral arms, the toroidal halo, the X-shaped field and the compressed field of the Local Bubble wall.