Week 27.11.2023 – 03.12.2023

There has recently been a lot of activity in the field of generalised symmetries. In the context of supersymmetric gauge theories with interesting moduli spaces of vacua, such as 3d N=4 theories, global symmetries may enjoy a geometric interpretation: they act as isometries of the moduli space. In this talk I will informally put forward the idea that by enhancing the notion of moduli space one can in a similar fashion geometrise generalised symmetries. I will focus on simple 3d N=4 abelian example and talk about various things including what I'll call 0- and 1-form resolutions as well as automorphism 2-groups.

I will discuss a connection between harmonic analysis on hyperbolic n-manifolds and conformal field theory in n-1 dimensions. Used in one direction, this connection leads to new spectral bounds on hyperbolic manifolds. Used in the other direction, it offers a new viewpoint on the spectra data of conformal field theories.

Higher-order gravities are extensions of General Relativity (GR) which introduce in the classical action terms of higher order in the curvature. These appear naturally in the context of string effective actions, as well as in generic gravitational EFTs. Among the myriads of higher-order gravities one may think of, in this talk I will focus on specific theories whose equations of motion are of second order in derivatives for some particular backgrounds. I will provide many examples of such theories, classification results and argue that a subclass of them actually forms a basis for the space of gravitational EFTs. Afterwards, I will discuss the addition of non-minimal couplings to matter, show that some of these theories possess fully regular black hole solutions and conclude with some holographic applications.

We discuss the initial boundary value problem in general relativity (with vanishing cosmological constant). We consider a non-standard set of boundary conditions, known as conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed at the boundary. We compare these results with analogous results for the Dirichlet problem both in Lorentzian and Euclidean signature, where a notion of conformal black hole thermodynamics will be developed. Time permitting, we will discuss implications for holography and de Sitter space.