In this talk we present a proof for the fundamental question raised by W. Kohnen and N.P Skoruppa in the year 1989 in their Joint work and there by we get a proof of analytic continuation and functional equation for the associated spinor zeta function of a given Hecke eigenform F -a Siegel cusp form of weight k for the full group of degree two. Google meet link: meet.google.com/tmu-xnov-cge

After an initial exponentially fast period of expansion ("inflation"), the content of the universe as we know it today is created by transferring the energy responsible for inflation into standard model particles. This phase of "preheating" is dominated by non-linear classical physics and has to be resolved numerically. After reviewing this problem, I will present CosmoLattice, a user-friendly, modern, parallelized and versatile C++ framework to perform such simulations, with scalar, Abelian and non-Abelian fields. I will also explain how this framework is particularly adequate to develop any kind of new software operating with "fields" on lattices, be them related to cosmology or not.

With the announcement of tens of detections of compact binary mergers by the LIGO-Virgo-Kagra collaboration, there is no doubt that gravitational-wave (GW) astronomy has well and truly arrived. Remarkably, GW astronomy interfaces organically with a number of important and established branches of astrophysics and cosmology, which I will demonstrate over the course of this talk. I will also elaborate on some key aspects of GW detection and inference. These include distinguishing true signals from noise transients, astrophysical classification of candidate events, inferring rates of compact binary mergers, constraining models of compact binary populations with GW data, enhanced GW-early warning and the rapid inference of a source's sky-location, and placing GW data-driven constraints on aspects of early-Universe models. google meet link: meet.google.com/yzy-ueat-dow