Talks

The local and global properties of the retarded and Feynman Green functions to the wave equation in curved spacetime are crucial for radiation reaction in the classical theory and for renormalisation in the quantum quantum theory. Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental geometrical bitensors determining the local Hadamard singularity structure of these Green’s functions. We illustrate their use in a semi-recursive approach showing how to determine covariant expansions to high order, for example, calculating the tail term reflecting backscattering by the curvature of spacetime to 20th order in the geodesic separation in a matter of minutes, and as the basis of numerical calculations. We also present an efficient method to construct covariant expansions of the tail term, without using the formal Hadamard light-cone expansion. Finally we discuss the relationship between the geodesic structure, quasi-normal modes with associated excitation factors and the global behaviour of Green functions in black hole space-times.

We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites useful for quantum computation and multi-party quantum communication. We observe that the key features of the entanglement dynamics of the composite spin chain are remarkably well described using a simple model of two singlets, each formed by two spins. The proposed entanglement routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physical settings.

In the last many years a number of metallic solids have been studied that defy understanding within the principles of conventional textbook solid state physics. The most famous are the cuprate high temperature superconductors though many other examples have been found. In this talk I will argue that the mysterious properties of many such materials arises from an imminent `death' of their Fermi surfaces. I will discuss some theoretical ideas on how to kill a Fermi surface, and their implications for experiments.

Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question of why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely. This is based to a large extent on Lucien Hardy's seminal work. We start with the framework of "general probabilistic theories", a simple, minimal mathematical description for outcome probabilities of measurements. Then, we use group theory and convex geometry to show that the state space of a bit must be a 3D (Bloch) ball, finally recovering the Hilbert space formalism. There will also be some speculation on how to find natural post-quantum theories by dropping one of the axioms.

It is commonly believed that the current problems in the capital markets are a result of the financial models developed by academic mathematicians and industry practitioners. In fact, many of us have been pointingout for years that banks were involved in very risky activities, which produced illusory short term profits. In this talk, I will give a short introduction to the theory behind pricing and hedging derivative contracts (options). A derivative contract is based on an underlying asset. The standard model for the underlying asset price movement assumes that prices evolve according to a random walk with a drift. It is possible for an option seller to set up a hedging portfolio, which is then dynamically rebalanced in response to changes in the underlying asset price. Then, regardless of the random movement of the asset price, the seller of the option is able to pay out the value of the this contract at expiry. There is strong evidence that the normal market behavior assumed by standard models is punctuated by occasional large jumps or drops in prices (e.g. subprime mortgages). These processes are called "jump diffusion" models. A simulation of a trading strategy which exploits these market characteristics shows that bankers can produce apparent profits for many years, followed by enormous losses. The compensation system widely used in the financial sector encourages these sorts of activities. In essence, this bonus system allows executives and traders to be rewarded for apparent short term profits, and to walk away unscathed after producing staggering losses.