I will continue the discussions on line defects and surface defects in class S theories, making connections to the construction of the quantum trace map, as well as to the exact WKB method for higher order ODEs.

In the first part of my talk I'll briefly review some aspects of the relations between N=4, d=4 SYM and vertex operator algebras (VOAs) discussed in recent work of Gaiotto and collaborators. The resulting picture predicts conjectural generalisations of the geometric Langlands correspondence. We will focus on a class of examples figuring prominently in recent work of Creutzig-Dimofte-Garner-Geer, labelled by parameters n (rank) and k. For the case k=1,n=2 we will point out that the conformal blocks of the relevant VOA, twisted by local systems, represent sections of natural holomorphic line bundles over the moduli spaces of local systems closely related to the isomonodromic tau functions. Observing the crucial role of (quantised) cluster algebras in the definition of the holomorphic line bundles suggests natural generalisations of this story to higher values of the parameters k and n.

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.