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A quantum entanglement is a special kind of correlation; it may yield a strong correlation that is not possible in a classical ensemble, or hide the correlation from all local observables. Especially important is the entanglement that arises from local interactions for its implications in many-body physics and future’s quantum technologies.
I will review a few characteristics of entangled qubits in connection to fault-tolerant quantum information processing, and present a class of long-range entangled many-body states that are ground states of gapped local Hamiltonians on lattices. The class is qualitatively unconventional in many ways, and substantially boosts the richness of many-body entanglement. Implications in mechanisms of localization, renormalization group flow, quantum information storage, and topological order will be discussed.

Topological phases of matter are phases of matter which are not characterized
by classical local order parameters of some sort. Instead, it is the global properties
of quantum many-body ground states which distinguish one topological phase from
another. One way to detect such global properties is to put the system on a topologically
non-trivial space (spacetime). For example, topologically ordered phases in (2+1)
dimensions exhibit ground state degeneracy which depends on the topology of the spatial manifold.
In this talk, I will discuss how one can use a {\it unoriented} space (spacetime)
to detect non-trivial properties of topological phases of matter in the presence
of discrete spacetime symmetry, such as time-reversal or reflection symmetry.
In particular, I will show how interaction effects on topological insulators and
superconductors can be understood using quantum anomalies on unoriented spacetime.

After the completion of the Planck satellite, the next most important experiments in cosmology will be about mapping the Large Scale Structures of the Universe. In order to continue to make progress in our understanding of the early universe, it is essential to develop a precise understanding of this system. The Effective Filed Theory of Large Scale Structures provides a novel framework to analytically compute the clustering of the Large Scale Structures in the weakly non-linear regime in a consistent and reliable way. The theory that describes the long wavelength fluctuations is obtained after integrating out the strongly-coupled, short-distance modes, and adding suitable operators that allow us to correctly reconstruct the effect of short distance fluctuations at long distances. By using techniques that originate in the particle physics context, a few observables have been computed so far, and the results are extremely promising. I will discuss the formalism, the main results so far, and the potential implications for next generation experiments.