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In order for quantum fluctuations during inflation to be converted to classical stochastic perturbations, they must couple to an environment which produces decoherence. Gravity introduces inevitable nonlinearities or mode couplings. We study their contribution to quantum-to-classical behavior during inflation. Working in the Schrodinger picture, we evolve the wavefunctional for scalar fluctuations, accounting for minimal gravitational nonlinearities.  The reduced density matrix for a given mode is then found by integrating out shorter-scale modes. We find that the nonlinearities produce growing phase oscillations in the wavefunctional, which decohere the single-mode reduced density matrix into a diagonal mixed state. However, the weakness of the coupling delays decoherence until the mode is much longer than the Hubble scale environment modes. In summary, the gravitational coupling of long and short scales is sufficient to produce a mixed state of classical perturbations during inflation.

String theory is starting to provide novel all-loop precision tools for the computation of scattering amplitudes in the high energy (HE) limit of N=4 SYM theory. After a review of some key insights and results for hexagon amplitudes, I will describe ongoing developments addressing higher numbers of external gluons.

I will discuss how to classify (up to discrete identifications) all rigid 4D N=2 supersymmetric backgrounds in both Lorentzian and Euclidean signatures that preserve eight real supercharges. These include backgrounds such as warped S_3×R, warped AdS_3×R, and AdS_2×S^2, as well as some more exotic geometries. I will also address how to construct all supersymmetric two-derivative actions involving hypermultiplets and vector multiplets in these backgrounds.