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Multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols. However obtaining a generic, structural understanding of entanglement in N-qubit systems is still largely an open problem. Here we show that multipartite quantum entanglement admits a compositional structure. The two SLOCC-classes of genuinely entangled 3-qubit states, the GHZ-class and the W-class, exactly correspond with the two kinds of commutative Frobenius algebras on C^2, namely `special' ones and `anti-special' ones. Within the graphical language of symmetric monoidal categories, the distinction between `special' and `anti-special' is purely topological, in terms of `connected' vs.~`disconnected'. These GHZ and W Frobenius algebras form the primitives of a graphical calculus which is expressive enough to generate and reason about representatives of arbitrary N-qubit states. This calculus induces a generalised graph state paradigm for measurement-based quantum computing, and refines the graphical calculus of complementary observables due to Duncan and one of the authors [ICALP'08], which has already shown itself to have many applications and admit automation. References: Bob Coecke and Aleks Kissinger, http://arxiv.org/abs/1002.2540

These three lectures cover several ideas of physics beyond the Standard Model. My focus is on ideas that give a natural stabilization solution to the electroweak scale, which is mysteriously light compared to the gravitational Planck scale. These ideas include supersymmetric field theories, extra dimensions, and Higgs boson physics. I shall describe what I think are the "best bets" among these approaches, and more importantly the ways they can be discerned by experiment. Special emphasis will be on theories that can be confirmed at the Large Hadron Collider (LHC) that is just now starting.

Gamma rays from WIMP annihilation are an important signal through which we search for non-gravitational interactions of dark matter. In particular, lines in the energy spectrum of gamma rays provide a signal which is difficult for conventional astrophysics to fake, and are thus promising despite the fact that such lines are generically expect to be suppressed, arising from one loop processes. I will discuss two theories which have an interesting family of gamma ray lines and discuss how such lines can reveal information about the WIMPs and the dark sector.

A quantum theory of gravity implies a quantum theory of geometries. To this end we will introduce different phases spaces and choices for the space of discretized geometries. These are derived through a canonical analysis of simplicity constraints - which are central for spin foam models - and gluing constraints. We will discuss implications for spin foam models and map out how to obtain a path integral quantization starting from a canonical quantization.

Gas accretion onto black holes is thought to power some of the most energetic astrophysical phenomena observed. Black hole accretion disks are efficient engines for converting binding energy into light, and for launching relativistic unbound flows (jets) such as in gamma ray bursts, microquasars and radio-loud active galactic nuclei (AGN). Some systems individually exhibit a wide variety of spectral and bolometric states while others remain remarkably predictable. As their brightest emission usually emanates near the black hole's event horizon, they serve as excellent environments for exploring different theories of gravity or for constraining the black hole's geometry. In this talk I will explain how investigators use modern general relativistic magnetohydrodynamic computer simulations to understand accretion observations and probe the strong-field regime of gravity. In particular, I will focus on three topics. First, I will describe how dynamical models of the accretion flow around Sagittarius A*, the supermassive black hole at the center of our galaxy, can help us predict what we will see when observations at the sub-horizon scale are made soon for the first time. Second, I will explain recent developments in simulating cooled thin disks and how their results may affect estimates of black hole spin from the disks' thermal spectra. Last, I will describe how temporal variability analysis of our dynamical simulations can offer insight into the common behavior seen in high-energy emission from black holes with masses of 10 solar masses to a billion solar masses.