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.

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

Over the past decade, many infrared phenomena of gauge theories, such as soft theorems and memory effects, have been shown to be manifestations of asymptotic symmetries which persist to the spacetime boundary. In this talk, I will discuss ongoing work, in collaboration with Robert Myers and Ana-Maria Raclariu, which recasts the asymptotic symmetries of gauge theories in Minkowski spacetime through conformal mappings. Through a mapping to the Einstein static universe, I will describe how conservation of asymptotic charge can be viewed as a smoothness constraint for image sources passing through spacelike infinity. Additionally, I will sketch how asymptotic charge flux through a subregion of null infinity is mapped to edge modes. This will then allow us to quantify fluctuations in asymptotic charge flux by relation to edge mode entropies, which have been well-studied in literature. Altogether, the general theme of my talk will be how new insights can be obtained by conformally mapping asymptotic structures of gauge theories to various settings.

The detection of gravitational waves has opened up new observational windows into the physics of black holes and has the potential to shed light on how imposing unitary evolution modifies the near horizon dynamics. In this talk, I will present how recent developments in holography have provided a way of understanding the physics of black hole thermalization in terms of the spacing statistics of black hole microstates. Based on this, I will suggest that the issue of measuring the quantum aspects of black holes from their ringdown depends on the spectral statistics of their microstates. I will then suggest that certain microstate statistics lend to the possibility of deviations in the ringdown behaviour of black holes in the form of “echoes” which might be interpreted as being due to Planck-scale microstructure near the horizon.

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.

Many non-trivial ideas have been proposed to resolve singularities in quantum gravity. In this talk I argue that singularity resolution can be trivial in gravitational path integrals, because geodesically incomplete singular spacetimes are usually not included in the sum. For theories where this holds, there is no need to develop non-trivial ideas on singularity resolution. Instead, efforts should better be directed to understand tunneling processes and complex-valued spacetimes.