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In 1965, Lévy-Leblond introduced the ultra-relativistic cousin of the Poincaré symmetry and named it the Carrollian symmetry after Lewis Carroll (the pseudonym of the author of Alice’s adventures in Wonderland and Through the Looking-Glass). It can be seen as the counterpart of the non relativistic Galilean symmetry. Since then, Carrollian symmetry has become an active research topic in various fields, ranging from field theories, hydrodynamics, and more recently, gravity and black holes. In this talk, I will give an introductory review of the Carrollian symmetry and Carrollian physics, especially focusing on the emergence of Carrollian hydrodynamics in gravity and black holes

I will discuss work-in-progress for defining a new proposal for the covariant holographic entanglement entropy. The proposal instructs us to find maximal spacelike codimension-2 surfaces on timelike hypersurfaces in the bulk, followed by a minimization among all possible hypersurfaces in the right homology class. We describe and prove various properties of such minimax surfaces, and argue for their equivalence with the more familiar HRT and maximin proposals. Finally, we give compelling reasons to be interested in yet another entanglement entropy proposal: minimax surfaces allow us to prove all higher entropy cone inequalities, showing that the RT and HRT holographic entropy cones are indeed equivalent.

We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time.

For nearly a century, we have known that the majority of matter in the universe is not luminous. In the past few decades we have come to be certain that this matter is not only not luminous but not made out of any of the particle ever observed in a laboratory. I will describe the ongoing hunt for this matter and the prospects for the discovery in the next decade. I will further discuss recent claims the dark matter may have been discovered in various signals, and prospects for resolving these claims in the next few years. Finally I will touch on the idea of "dark forces," the idea of an expansive dark sector that is much greater than a single dark particle.

I will give an introduction to 4d N=2 class-S theories. I will describe the construction of such theories, the roles played by extended defects such as line defects and surface defects, as well as connections to Hitchin systems.