Talk Details

Marek Liška: Semiclassical Spacetime Thermodynamics 

I outline the recovery of semiclassical gravitational dynamics from entanglement equilibrium of local causal horizons. Due to backreaction of quantum fields, gravitational entanglement entropy acquires corrections encoded in the conformal anomaly. Though entropy is no longer simply proportional to area, the universal nature of the anomaly still ensures a robust entropy prescription that can be obtained without invoking the gravitational Lagrangian. Then, gravitational dynamics follows from equilibrium conditions in a self-contained and internally consistent way. I further discuss the potential of applying the formalisms of von Neumann algebras and quantum reference frames in this context. While the talk focuses on the most tractable 2D case, I also comment on the physically most relevant 4D case. 

Liam Featherly: Why Causal Sets?

The breakdown of the continuum hypothesis at the Planck scale, manifested by UV divergences in QFT and singularities in General Relativity, suggests that spacetime may be fundamentally discrete. This talk introduces Causal Set Theory, an approach to quantum gravity where the smooth Lorentzian manifold is replaced by a locally finite partial order. 

We begin by motivating discreteness not merely as a mathematical regulator, but as a physical necessity motivated by arguments from black hole entropy and information theory. We contrast Causal Sets with regular lattice discretizations, demonstrating how "sprinkling" points via a Poisson process preserves Lorentz invariance. We then explore the core tenet of the theory—"Order + Number ~ Geometry"—showing how familiar geometric concepts like geodesics, dimension, and the Einstein-Hilbert action (via the Benincasa-Dowker formalism) can be recovered purely from the causal relations and counting of vertex elements. Finally, we discuss the statistical behavior of these sets in the large-$N$ limit, specifically the dominance of non-manifold-like Kleitman-Rothschild orders, and the work being done to distinguish, at a graph theoretic level, the differences between these KR orders and manifold-like causal sets. 

Joshua Jones: Entanglement Entropy in Spacetime, and a Signature of Discreteness 

Entanglement entropy is one of the key candidates for the Bekenstein-Hawking entropy of black holes, although it is well known to be divergent without a regularisation scheme. Such a scheme likely originates in nature from quantum gravity. If one has a covariant theory of quantum gravity, one requires a means of performing the calculation of entanglement entropy in spacetime, so as to actually apply the scheme faithfully. I will give such a spacetime formulation of entanglement entropy for quasifree fields, and show a potential regularisation originating from a theory of quantum gravity, causal set theory. It will be seen that upon calculation, the entanglement entropy carries within it a signature of the causal set discreteness. 

Denjoe O'Connor: Counting States in Gauge Orthogonal Invariant Matrix Models and Possible Connections with Black Hole Entropy in anti de Sitter Spacetimes

Gauge gravity indicates that anti de Sitter spacetimes with black holes emerge from gauged matrix models. I will endeavour to connect these ideas by focusing on the microcanonical description of the relevant states in the simplest matrix models where there are indications of this connection.