I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

The graph C*-algebra construction associates a unital C*-algebra to any directed graph with finitely many vertices and countably many edges in a way which generalizes the fundamental construction by Cuntz and Krieger. We say that two such graphs are C*-equivalent when they define isomorphic C*-algebras, and give a description of this relation as the smallest equivalence relation generated by a number of "moves" on the graph that leave the C*-algebras unchanged. The talk is based on recent work with Arklint and Ruiz, but most of these moves have a long history that I intend to present in some detail.

In this talk I will explain how a subfactor (ie an inclusion of type II_1 factors) give rise to a diagrammatic algebra called the Temperley-Lieb-Jones algebra. We will observe the connection between the index of the subfactor, and the TLJ algebra. In the TLJ algebra setting, we will observe that indices below four are discrete, while any number above four can be an index.

A well-behaved field theory living on a fixed background has a causality structure defined by the background metric. In holography, however, signals can travel through the bulk, and some bulk metrics would allow a signal to travel faster than the speed of light as seen on the boundary. These are called boundary causality violating metrics. Holographers usually work with a classical bulk metric, in which case they declare that boundary causality violating metrics are forbidden. However, in a full quantum gravity path integral, these metrics do contribute. The question is then: how to avoid causality violation in this context? In this talk I will give a prescription that achieves this.

I will discuss a string theory perspective on the Bethe/Gauge correspondence for the XXX superspin chain. I explain how to realize 4d Chern-Simons theory with gauge supergroup using branes, and how the brane configurations for the superspin chain get mapped to 2d N = (2,2) quiver gauge theories proposed by Nekrasov. This is based on my ongoing work with Nafiz Ishtiaque, Faroogh Moosavian and Surya Raghavendran.

I will discuss a precise connection between renormalization group (RG) and quantum chaos. Every RG flow between two conformal fixed points can be described in terms of the dynamics of Nambu-Goldstone bosons of broken symmetries. The theory of Nambu-Goldstone bosons can be viewed as a theory in anti-de Sitter space with the flat space limit. This enables an equivalent formulation of these 4d RG flows in terms of spectral deformations of a generalized free CFT in 3d. This approach provides a precise relation between C-functions associated with 4d RG flows and certain out-of-time-order correlators that diagnose chaos in 3d. As an application, I will show that the 3d chaos bound imposes constraints on the low energy effective action associated with unitary RG flows in 4d with a broken continuous global symmetry in the UV. These bounds, among other things, imply that the proof of the 4d a-theorem remains valid even when additional global symmetries are broken.