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Shared entanglement between sender and receiver can enable more errors to be corrected than with a standard quantum error-correcting code. This extra error correction can be used either to boost the rate of the code--commonly seen in quantum codes constructed from classical linear codes--or to increase the error-correcting power of the code (as represented by, for example, the code distance). We will see how adding extra entanglement to a given quantum code can increase its distance, and discuss the optimization problem in maximizing the effectiveness of a given amount of added entanglement. We will also briefly examine some applications of entanglement-assistance to particular types of codes, such as LDPC codes and convolutional codes.

The primordial density fluctuations that seeded large-scale structure are known to be nearly Gaussian, as predicted by most early universe models like slow-roll inflation. Many of these models predict a small (but nonzero!) amount of primordial non-gaussianity, which can subtly affect the statistics of CMB anisotropies. Surprisingly, even a small primordial non-gaussianity can produce enormous changes in the large-scale clustering of galaxies and quasars at late times. I will describe the origin of this effect, and review recent constraints on non-gaussianity using measurements of the clustering of galaxies and quasars in SDSS.

We discuss a candidate mechanism through which one might address the various cosmological constant problems. We observe that the renormalization of gravitational couplings manifests non-local modifications to Einstein's equations as quantum corrected equations of motion, and in doing so offers a complimentary realization of the degravitation paradigm-- a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider theories whose coupling to gravity might a priori induce non-trivial RG flow for gravitational couplings in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton's constant upon subsequently being integrated out.