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How well can we predict our future climate? If the flap of a butterfly’s wings can change the course of weather a week or so from now, what hope trying to predict anything about our climate a hundred years hence? In this talk I will discuss the science of climate change from a perspective which emphasises the chaotic (and hence uncertain) nature of our climate system. In so doing I will outline the fundamentals of climate modelling, and discuss the emerging concept of inexact supercomputing, needed - paradoxically perhaps - if we are to increase the accuracy of predictions from these models. Indeed, revising the notion of a supercomputer from its traditional role as a fast but precise deterministic calculating machine, may be important not only for climate prediction, but also for other areas of science such as astrophysics, cosmology and neuroscience.

In this talk I will: 1) review the results of my work on a geometric approach to foundations for a postquantum information theory; 2) discuss how it is related to other foundational approaches, including some resource theories of knowledge and quantum histories; 3) present some of my research on a category theoretic framework for a multi-agent information relativity. More details on part 1: this approach does not rely on probability theory, spectral theory, or Hilbert spaces. Normalisation of states, convexity, and tensor products are allowed but not assumed foundationally. Nonlinear generalisation of quantum kinematics and dynamics is constructed using geometric structures (quantum relative entropies and Banach Lie--Poisson structure) over the sets of quantum states on W*-algebras. In particular, unitary evolution is generalised to nonlinear hamiltonian flows, while Lueders' rules are generalised to constrained relative entropy maximisations. Combined together, they provide a framework for causal inference that is a generalisation and replacement for completely positive maps, with information dynamics determined directly by epistemic constraints, and no requirement for lack of correlation. Orthodox probability theory and quantum mechanics are special cases of this framework. I will also give the progress report on the reconstruction conjecture: given the category of sets of abstract "states" equipped with the suitably defined entropic distances and BLP structure, how one reconstructs the W*-algebraic case? The discussion of the consistent operational semantics for this approach will lead us to the parts 2 and 3.

In the study of closed quantum system, the simple harmonic oscillator is ubiquitous because all smooth potentials look quadratic locally, and exhaustively understanding it is very valuable because it is exactly solvable.  Although not widely appreciated, Markovian quantum Brownian motion (QBM) plays almost exactly the same role in the study of open quantum systems.  QBM is ubiquitous because it arises from only the Markov assumption and linear Lindblad operators, and it likewise has an elegant and transparent exact solution. QBM is often introduced with specific non-Markovian models like Caldeira-Leggett, but this makes it very difficult to see which phenomena are universal and which are idiosyncratic to the model.  Like frictionless classical mechanics or nonrenormalizable field theories, the exact Markov property is aphysical, but handling this subtlety is a small price to pay for the extreme generality.   The widest class of QBM dynamics is symplectic invariant and includes Einstein-Smoluchowski diffusion, damped harmonic oscillations, and pure spatial decoherence as special cases, whose close relationship is often obscured. 

In previous work it has been observed that the singularity structure of multi-loop scattering amplitudes in planar N=4
super-Yang-Mills theory is evidently dictated by cluster algebras. In my talk I will discuss the interplay between this mathematical
observation and the physical principle that the singularities of Feynman integrals are encoded in the Landau equations.

Effective field theories (EFT) are everywhere in particle physics. Given an EFT, the first question we ask is “what are all the operators consistent with the symmetries and degrees of freedom at a particular expansion order? In this talk I will show how this question can be attacked, and often answered, using an object called a Hilbert series.

I will discuss the recent progress on understanding scattering amplitudes in N=4 SYM beyond the planar limit. I will show that the singularity structure of these amplitudes is very similar to the planar amplitudes suggesting new hidden symmetries to be present in the complete N=4 SYM theory. I will also talk about the extension of this work to N=8 SUGRA by studying the on-shell diagrams in this theory as well as some of the properties of the integrands of loop amplitudes.

Topological insulators (TIs) are a recently discovered state of matter characterized by an “inverted” band structure driven by strong spin-orbit coupling. One of their most touted properties is the existence of robust "topologically protected" surface states.  I will discuss what topological protection means for transport experiments and how it can be probed using the technique of time-domain THz spectroscopy applied to thin films of Bi2Se3.  By measuring the low frequency optical response, we can follow their transport lifetimes as we drive these materials via chemical substitution through a quantum phase transition into a topologically trivial regime[1].  I will then discuss our work following the evolution of the response as a function of magnetic field from the semi-classical transport regime[2] to the quantum regime[3].  In the semi-classical regime, an anomalous increase of the transport scattering rate was observed at high field, which contribute from electron-phonon interaction[2].  In the highest quality samples[3,4], we observe a continuous crossover from a low field regime where the response is given by semi-classical transport and observed in the form of cyclotron resonance to a higher field quantum regime[3].  In the later case, we find evidence for Faraday and Kerr rotation angles quantized in units of the fine structure constant[3].  This quantized rotation angle can be seen as evidence for a novel magneto-electric of the TI’s surface e.g. the much heralded axion electrodynamics of topological insulators.  Among other aspects this give a purely solid-state measure of fine structure constant[3].

1. Wu, et al, Nat. Phys. 9, 410 (2013).

2. Wu, et al, Phy. Rev. Lett. 115, 217602  (2015).

3. Wu, et al, arXiv. 1603.04317 (2016)

4. Nikesh, et al, Nano. Lett. 15, 8245 (2015)