We will discuss two aspects of black hole perturbation theory: symmetries of static perturbations around black holes which underpins the vanishing of the tidal Love numbers, and nonlinear quasi-normal modes during black hole ringdown. 

Dark matter in the Universe can be considered as a collisionless self-gravitating fluid obeying the Vlasov-Poisson equations. In the standard picture of cosmic structure formation, the first dark matter objects to form are expected to be microhalos of roughly Earth mass and solar system size. These halos can subsequently merge to form larger dark matter halos such as that of our Galaxy. In practice, resolving dark matter dynamics relies on a N-body approach, but with the advent of exaflopic computers it now becomes possible to solve directly Vlasov dynamics in six-dimensional phase-space.

Since the discovery of the Higgs boson 12 years ago, terrestrial particle collider experiments have encountered a slowdown in the quest for physics beyond the Standard Model. Arguably, the upcoming decade promises a paradigm shift towards exploring high-energy physics through cosmological observations. With an abundance of data, independent datasets, and improved systematics, a new era of exploration unfolds. Theorists now strive to attain the precision level demanded by upcoming experiments.

I will discuss black holes in the context of Einstein–aether and khronometric gravity — two closely related alternative theories of gravity that allow violations of local Lorentz invariance. Since these theories admit faster-than-light propagation, metric horizons are generically permeable and it is not clear whether proper black holes can exist; surprisingly, in some cases they do, thanks to the appearance of a new kind of “universal” horizon. I will review past and recent results on the topic, with a particular emphasis on the difficulty of finding rotating solutions.

As is well known, the string spectrum comprises infinitely many states that can collectively be visualized along Regge trajectories of increasing mass and spin. Its massless and lightest levels, as well as certain higher spins including the leading Regge trajectory, have been the focus of past studies. In principle, access to any state is possible, but the traditional methodology is non-covariant and does not immediately lead to irreducible representations of the Wigner little group. In this talk, we will discuss a new and covariant technology of constructing the string spectrum.