**William Donnelly**

**Entanglement Entropy in Loop Quantum Gravity**

The entanglement entropy between quantum fields inside and outside a black hole horizon is a promising candidate for the microscopic origin of black hole entropy. I will explain the motivation behind this interpretation of black hole entropy, and why it requires quantum gravity. I will then apply these ideas to loop quantum gravity and show how to compute the entanglement entropy of spin network states. The result of this calculation agrees asymptotically with results from the isolated horizon framework, and I will give the reason for this agreement. Finally, I will show that the entanglement entropy gives extensive corrections to the area law, suggesting corrections to the gravitational action.

**Cohl Furey**

**Division Algebras**

The normed division algebras over the reals are: R, the complex numbers, quaternions and octonions. The aim of this talk is to show that (1) the division algebras are interesting in their own right and (2) they are useful in physics beyond R and C. In particular, we show a more concise representation of Lorentz transformations, which act on complex-quaternionic numbers.

**Isabeau Premont-Schwarz**

**Penrose's Space of Quantized Directions**

In the sixties, Roger Penrose came up with a radical new idea for a quantum geometry which would be entirely background independent, combinatorial, discrete (countable number of degrees of freedom), and involve only integers and fractions, not complex or real numbers. The basic structures are spin-networks. One reason we might believe that space or space-time might be discrete is that current physique tells us that matter is discrete and that matter and geometry are related through gravity. Once a discrete theory is decided on, it seems awkward that the dynamics would retain "continuous elements" in the form of real numbers (used for the probabilities for example). The great achievement of Penrose's theory is that there is a well defined procedure which gives the semi-classical limit geometry (always of the same dimension) without any input on topology (the fundamental theory does not contain a manifold).

**Filippo Passerini**

**Wilson Loops as D-Branes**

Using the AdS/CFT correspondence I will show that Wilson loop operators in a Yang Mills theory can be described as fundamental strings or D-branes in a dual string theory.

**Matthias Wapler**

**Charges from Attractors**

We describe how to recover the quantum numbers of extremal black holes from their near horizon geometries. This is achieved by constructing the gravitational Noether-Wald charges which can be used for non-extremal black holes as well. These charges are shown to be equivalent to the U(1) charges of appropriately dimensionally reduced solutions. Explicit derivations are provided for 10 dimensional type IIB supergravity and 5 dimensional minimal gauged supergravity, with illustrative examples for various black hole solutions. We further discuss how to derive the thermodynamic quantities and their relations explicitly in the extremal limit, from the point of view of the near-horizon geometry. We relate our results to the entropy function formalism.

**Yidun Wan**

**Propagation and interaction of topological invariants on embedded 4-valent spinets**

The study of particle-like excitations of quantum gravitational fields in loop quantum gravity is extended to the case of four valent graphs and the corresponding natural evolution moves based on the dual Pachner moves. This makes the results applicable to spin foam models. We find that some braids propagate on the networks and they can interact with each other, by joining and splitting. The chirality of the braid states determines the motion and the interactions, in that left handed states only propagate to the left, and vise versa.

**Lucy Zhang **

**Learning about topological quantum memory**

I will introduce Kitaev's suface codes as a block quantum error-correcting code. Recovery procedures will be described in the case of imperfect syndrome measurements. More might be covered if time permits.

**Joel Brownstein**

**Renormalization of Gravitation at Astrophysical Distances**

The asymptotic freedom conjecture for gravitation is explored in which strong renormalization effects may occur at distances greater than one astronomical unit. Nonperturbative renormalization group trajectories exhibiting such an infrared fixed point describe a theory of gravitation with a running gravitational coupling which grows at astronomical distances. The concept that this extra gravity may provide the answer to the missing mass inherent in the dark matter paradigm is a natural suggestion. We provide the alternative of Modified Gravity to answer the problem of galaxy rotation curves from the smallest dwarf galaxies to the largest giant galaxies and to galaxy clusters including the Bullet Cluster. The theory may also explain the apparent anomalous deceleration of the Pioneer 10/11 space probes, within solar system constraints.