This talk will review recent work on the non-perturbative structure of four-graviton scattering in maximally supersymmetric string theory in dimensions $D >2$. The complete moduli dependence of the higher derivative terms in the low energy expansion up to order d*6 R**4 is determined in terms of Eisenstein series and more general automorphic functions for the U-duality groups. These functions contain a wealth of information concerning perturbative and instanton effects, including the precise coefficients of the logarithmic ultraviolet divergences of supergravity in dimensions 8,7,6 at 1,2,3 loops, respectively. Furthermore, it will be argued that supersymmetry ceases to protect N=8 supergravity from a d*8 R**4 ultraviolet divergence at seven loops. This is based on several approaches - most notably a recent explicit construction of the five-loop four-graviton amplitude.

We study the cosmology of perturbative superstring theory during the radiation(-like) era for semi-realistic backgrounds with initial N=1 supersymmetry. This analysis is necessary for studying the electroweak phase transition within the framework of perturbative string cosmology, and is valid for times after the inflation era (or alternatively Hagedorn era) but before the electroweak symmetry breaking transition. We find that previous results for the N=2 case generalize; namely an attraction to a radiation-like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we find that both toroidal and orbifold directions never decompactify, except for special cases where toroidal cycles are wrapped by supersymmetry breaking fluxes. This suggests a mechanism for generating spatial directions during the radiation-like era.

AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index over states carrying a fixed set of charges grows as 1/N times the entropy of the black hole carrying the same set of charges. In this paper we verify this explicitly by calculating the microscopic Z_N twisted index for a class of states in the CHL models. This demonstrates that black holes carry more information about the microstates than just the total degeneracy.