I will explore subtle aspects of rank-one 4d N=2 supersymmetric QFTs through their low-energy Coulomb-branch physics. This low-energy Lagrangian is famously encoded in the Seiberg-Witten (SW) curve, which is a one-parameter family of elliptic curves. Less widely appreciated is the fact that various properties of the QFTs, including properties that cannot be read off from the Lagrangian, are nonetheless encoded into the SW curve, in particular in its Mordell-Weil group. This includes the global form of the flavour group, the one-form symmetries under which defect lines are charged, and the "global form" of the theory. In particular, I will discuss in detail the difference between the pure SU(2) and the pure SO(3) N=2 SYM theories from this perspective. I will also comment on 5d SCFTs compactified on a circle in this context.

I will discuss a KLT relation of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The goal is to introduce an interesting D-brane set up in the target space in order to accommodate both quantum numbers of the closed string. I will then discuss KLT factorization of amplitudes for winding closed strings in the presence of a critical Kalb-Ramond field and the relevance of this work for nonrelativistic string theory when taking the zero Regge limit. 

I will review some aspects of gravity in asymptotically flat spacetime and mention important challenges to obtain a holographic description in this framework. I will then present two important approaches towards flat space holography, namely Carrollian and celestial holography, and explain how they are related to each other. Similarities and differences between flat and anti-de Sitter spacetimes will be emphasized throughout the talk. 
 

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in AdS3 pure gravity, which we formulate as a topological quantum field theory. We explain how gravitational entropy can be viewed as bulk entanglement entropy of gravitational edge modes.  These edge modes transform under a quantum group symmetry. This suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.  Time permitting we will discuss a proposal for how our bulk TQFT arises from an ensemble of approximate CFT’s, generalizing the relation between JT gravity and random matrix ensemble.