I will discuss how the Higgs field of the Standard Model can make the Universe flat, homogeneous and isotropic; produce the quantum fluctuations seeding the structure formation; and lead to the Hot Big Bang. Together with neutral leptons the Higgs boson may play the crucial role in neutrino mass generation, baryogenesis and dark matter production.

We review recent results in open and closed superstring tree-level amplitudes. We establish a relation between open and closed string amplitudes communicated by some projection. As a consequence of the latter the alpha'-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. This map points into a deeper connection between gauge and gravity amplitudes than what is implied by the Kawai-Lewellen-Tye relations. The combination of single-valued projections, Kawai-Lewellen-Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang-Mills and supergravity theories

We discuss recent advances in understanding the quantum corrected moduli space of N=4 superconformal gauge theories in three dimensions. Monopole operators play an important role in the analysis. The results have applications ranging from mirror symmetry to the study of non Lagrangian theories.

I will discuss some aspects of inflation in supergravity. First, the scale of supersymmetry breaking is constrained in case of chaotic inflation. Second, the simplest inflationary models contain, in addition to the inflaton multiplet, another multiplet whose properties will be discussed.