43rd North British Mathematical Physics Seminar

Abstract: Conformal cyclic cosmology (CCC), initially proposed in 2005, takes what we currently regard as the entire history of the Universe, from its Big-Bang origin (but without any inflationary phase) to its final exponential expansion, to be but one aeon of a continual succession of such aeons. The big bang of each is taken to be a conformal continuation of the exponentially expanding remote future of the previous one via an infinite metric rescaling. A positive cosmological constant (dark energy) and some primordial scalar material (dark matter) are both essential to CCC's consistency. The 2nd law of thermodynamics is CCC's driving concept, and its consistency depends upon information loss in the quantum evaporation of black holes. Supermassive black hole encounters in the aeon previous to ours would have important observational implications for CCC, detectable within the cosmic microwave background. Evidence for this in both the WMAP and Planck satellite data will be presented.

Abstract: Entropy plays a central role in the understanding of processes in thermodynamic as well as in information theoretic systems. Due to the strong conceptual difference of thermodynamic and information theoretic entropy, however, their connection for microscopic systems is still not well understood. We study the application of an approach to thermodynamic entropy by Lieb and Yngvason to information-theoretic scenarios and establish a direct link between the Clausius entropy, known from phenomenological thermodynamics and the von Neumann entropy important for information theoretic scenarios on a microscopic scale. Simultaneously, entropic quantities relevant for thermodynamic non-equilibrium states are shown to correspond to the information-theoretic min- and max-entropies. The flexibility of our approach allows its application to a range of thermodynamic scenarios, leading to other thermodynamic potentials such as the free energy and its single shot variants.

Abstract: Abstract: Because of a shared link to matrix integration, there is an exploitable connection between the theory of finite-dimensional quantum systems and enumerative combinatorics. We demonstrate two methods for evaluating mean values of properties of bipartite quantum systems (in particular the trace of powers of the reduced density matrix), and show how these provide a powerful tool for building generating functions which enumerate classes of combinatorial objects called rooted hypermaps. This represents a significant increase in efficiency over existing methods for computing these generating functions, and may also provide some insight into the structure and behaviour of quantum systems.

Abstract: In many areas of geometry and physics we often require that the manifolds we work with carry a spin structure, that is a lift of the structure group of the tangent bundle from SO(n) to its simply connected cover Spin(n). In string theory and in higher geometry the analogue is to ask for a string structure; this is a further lift of the structure group to the 3-connected group String(n). Waldorf has given a way to describe string structures in terms of bundle gerbes (which are the abelian objects in higher geometry - a sort of categorification of a line bundle). Unfortunately, explicit examples are lacking. In this talk I will explain how all this works and give some examples of such structures. I will also explain some current work in progress on the geometry of string structures. This is joint work with David Roberts.

Abstract: Inspired by Twistor theoretic methods as applied to the computation of Scattering Amplitudes in N=4 SYM, we apply these methods to the computation of perturbative correlation functions of the chiral stress-tensor multiplet. In doing so, we find that the result can be expressed in terms of a simple building block which we can identify as a new class of off-shell superconformal invariant. In this talk, this new invariant will be discussed together with various features of the contributing `Twistor graphs' to the super-correlator, particularly in view of the so-called super-correlator/super-amplitude duality.

Abstract:Entanglement entropy is a very important quantity in holography, nevertheless it is only a measure of the total amount of entanglement between two complementary subsystems in a global pure state. Recent arguments suggest that a more detailed knowledge about the pattern of entanglement is essential for a deeper understanding of the relation between the bulk classical geometry and quantum information in the boundary theory. I will review some of these arguments and discuss how negativities and other measures can be used to extract additional information on the structure of entanglement.