Colloquium

The Standard model of Cosmology consists of a package of ideas that include Cold Dark Matter, Inflation, and the existence of a small Cosmological Constant. While there is no consensus about what lies beyond the Standard Model, there is a leading candidate that also includes a small package of ideas: A Landscape of connected vacua: the idea that the universe started out with a large energy density, and Coleman DeLuccia Tunneling between vacua. An additional idea that comes from string theory and black hole physics is the Holographic Principle. I will explain how the various ingredients for a "post-standard-model" standard model fit together.

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the first application of his concept of phase space, and the prototype of the conical intersections and fermionic sign changes that now pervade physics and chemistry. But the fine structure of the bright cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena arise when chirality and absorption are incorporated in addition to biaxiality.

Cosmologists are struggling to understand why the expansion rate of our universe is now accelerating. There are two sets of explanations for this remarkable observation: dark energy fills space or general relativity fails on cosmological scales. If dark energy is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $dlnG/dlna = \Omega^\gamma$, where $\Omega$ is the matter density independent of scale in a dark matter plus dark energy model. By combining measurements of the amplitude of redshift space, $\beta = (1/b) dlnG/dlna$ with measurements of galaxy bias, $b$, from cross-correlations with CMB lensing, redshift surveys will be able to determine the logarithmic growth rate as a function of scale and redshift. I will discuss the role of upcoming surveys in improving our ability to understand the origin of cosmic acceleration.

Key notions from statistical physics, such as "phase transitions" and "critical phenomena", are providing important insights in fields ranging from computer science to probability theory to epidemiology. Underlying many of the advances is the study of phase transitions on models of networks. Starting from the classic ideas of Erdos and Renyi, recent attempts to control and manipulate the nature of the phase transition in network connectivity will be discussed. Next, the influence of self-organization on phase transitions will be presented, as well as connections between the jamming transition in models of granular materials and constraint satisfaction problems in computer science. Finally, turning to network growth, I will show that local optimization can play a fundamental role leading to the mechanism of Preferential Attachment, which previously had been assumed as a basic axiom and, furthermore, resolves a long standing controversy between Herb Simon and Benoit Mandelbrot.

Yes, that's indeed where it happens. These pictures are not ordinary pictures but come with category-theoretic algebraic semantics, support automated reasoning and design of protocols, and match perfectly the developments in important areas of mathematics such as representation theory, proof theory, TQFT & GR, knot theory etc. More concretely, we report on the progress in a research program that aims to capture logical structures within quantum phenomena and quantum informatic tasks in purely diagrammatic terms. These picture calculi are faithful representations of certain kinds of monoidal categories, and structures therein. However, the goal of this program is partly to `release' these intuitive languages (or calculi) from their category-theoretic underpinning, and conceiving these pictures as mathematical entities in their own right. In this new language one is able to model and reason about things such a complementary observables, phase data, quantum circuits and algorithms, a variety of different quantum computational models, hidden-variable models, aspects of non-locality, and reason about all of these in terms of intuitive diagram transformations. Some recent benchmarks are the diagraamatic computation of quantum Fourier transform due to Duncan and myself, a purely diagrammatic proof of the no-cloning theorem due to Abramsky, and a categorical characterisation of GHZ-type non-locality due to Edwards, Spekkens and myself. For informal introductions we refer to: [1] Kindergarten quantum mechanics. http://arxiv.org/abs/quant-ph/0510032 [2] Introducing categories to the practicing physicist. http://arxiv.org/abs/0808.1032 For recent more advanced developments we suggest: [3] Selinger: Dagger compact closed categories and completely positive maps QPL\'05 http://www.mathstat.dal.ca/~selinger/papers.html#dagger [4] Coecke, Pavlovic, Vicary: A new description of orthogonal bases. http://arxiv.org/abs/0810.0812 [5] Coecke, Paquette, Perdrix: Bases in diagrammatic quantum protocols http://arxiv.org/abs/0808.1029 [6] Coecke, Duncan: Interacting quantum observables. ICALP\'08. http://www.springerlink.com/content/y443214116h76122/ [7] Coecke, Edwards: Toy quantum categories. QPL\'08. http://arxiv.org/abs/0808.1037

Integrability in gauge/string dualities will be reviewed in a broad perspective with a particular emphasis on the recently proposed equations describing the full planar spectrum of anomalous dimensions in AdS/CFT [N.Gromov, V.Kazakov, PV]. These are a concise version of Thermodynamic Bethe equations, called Y-system, which generalize the asymptotic Bethe equations of Beisert and Staudacher (which yield the full spectrum of N=4 SYM for asymptotically long local operators) and incorporate the 4-loop results for the shortest twist two operators obtained by Bajnok and Janik from the dual string sigma model (thus reproducing perturbative gauge theory computations with thousands of diagrams). On the way, we will explain some of the interesting open problems in the field.

Physicists are often so awestruck by the lofty achievements of the past, we end up thinking all the big stuff is done, which blinds us to the revolutions ahead. We are still firmly in the throes of the quantum revolution that began a hundred years ago. Quantum gravity, quantum computers, qu-bits and quantum phase transitions, are manifestations of this ongoing revolution. Nowhere is this more so, than in the evolution of our understanding of the collective properties of quantum matter. Fifty years ago, physicists were profoundly shaken by the discovery of universal power-law correlations at classical second-order phase transitions. Today, interest has shifted to Quantum Phase Transitions: phase transitions at absolute zero driven by the violent jigglings of quantum zero-point motion. Quantum, or Qu-transitions have been observed in ferromagnets, helium-3, ferro-electrics, heavy electron and high temperature superconductors. Unlike its classical counterpart, a quantum critical point is a kind of 'black hole' in the materials phase diagram: a singularity at absolute zero that profoundly influences wide swaths of the material phase diagram at finite temperature. I'll talk about some of the novel ideas in this field including 'avoided criticality' - the idea that high temperature superconductivity nucleates about quantum critical points - and the growing indications that electron quasiparticles break up at a quantum critical point.

Entanglement is one of the most fundamental and yet most elusive properties of quantum mechanics. Not only does entanglement play a central role in quantum information science, it also provides an increasingly prominent bridging notion across different subfields of Physics --- including quantum foundations, quantum gravity, quantum statistical mechanics, and beyond. Arguably, the property of a state being entangled or not is by no means unambiguously defined. Rather, it depends strongly on how we decide to regard the whole as composed of its part or, more generally, on the restricted ways in which we are able to observe and control the system at hand. Acknowledging the implications of such an operationally constrained point of view naturally has led to a notion of 'generalized entanglement,' which is directly based on quantum observables and offers added flexibility in a variety of contexts. In this talk, I will survey some of the main accomplishments of the generalized entanglement program to date, with an eye toward recent developments and open problems.

The fundamental laws of physics are very simple. The world about us is very complex. Living things are very complex indeed. This complexity has led some thinkers to suggest that living things are not the outcome of physical law but instead the creation of a designer. Here I examine how complexity is produced naturally in fluids.

The vacuum landscape of string theory can solve the cosmological constant problem, explaining why the energy of empty space is observed to be at least 60 orders of magnitude smaller than several known contributions to it. It leads to a 'multiverse' in which every type of vacuum is produced infinitely many times, and of which we have observed but a tiny fraction. This conceptual revolution has raised tremendous challenges in particle physics and cosmology. To understand the low-energy physics we observe, and to test the theory, we will need novel statistical tools and effective theories. We must also solve a long-standing fundamental problem in cosmology: how to define probabilities in an infinite universe where every possible outcome, no matter how unlikely, will be realized infinitely many times. This 'measure problem' is inextricably tied to the quantitative prediction of the cosmological constant.

Quantum graphity is a background independent condensed matter model for emergent locality, spatial geometry and matter in quantum gravity. The states of the system are given by bosonic degrees of freedom on a dynamical graph on N vertices. At high energy, the graph is the complete graph on N vertices and the physics is invariant under the full symmetric group acting on the vertices and highly non-local. The ground state dynamically breaks the permutation symmetry to translations and rotations. In this phase the system is ordered, low-dimensional and local. The model gives rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. In addition, in such a model, observable effects of emergent locality such as its imprint on the CMB can be studied. Finding the right dynamics for the desired ground state is ongoing work and I will review some of the basic results with an emphasis on the use of methods from quantum information theory such as topological order and the use of the Lieb-Robinson bounds to find the speed of light in the system.

Astronomers have discovered many candidate black holes in the universe and have studied their properties in ever-increasing detail. Over the last decade, a few groups have developed observational tests for the presence of event horizons in candidate black holes. The talk will discuss one of these tests, which indicates that the supermassive black hole at the center of our Galaxy must have a horizon.