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.

In General Relativity (GR), including Einstein-Maxwell theory, it is remarkable that all asymptotically flat black hole (BH) solutions have vanishing Love numbers. Consequently, the Love numbers of BHs present an excellent opportunity to examine any deviations from GR. We will investigate tidal deformations concerning neutral BHs and extremal BHs in EFT of gravity. In four dimensions, the primary contribution to the tidal Love numbers of neutral BHs arises from six derivative operators, while the Love numbers of extremal BHs are subject to corrections from four derivative operators.