We briefly review some models of dark energy. We start with the cosmological constant including models arising in string theory, before discussing dynamical models where a scalar field may be responsible for the observed late time acceleration. The possibility that we are not fully in control of the gravity sector is discussed and the possibility that the acceleration may be some manifestation of modified gravity on large scales is shown. All cases require some degree of fine tuning for the models to be compatible with observation. Finally, we briefly discuss some recent fun work involving scalar-tensor theories of gravity in which a self-tuning mechanism exists leading to the same late time cosmology independently of the size of the cosmological constant. Solutions include having radiation and matter dominated like regimes whilst the energy density remains dominated by a cosmological constant.

We will review the conjecture that the Kac-Moody Symmetry E_11 is an underlying symmetry of strings and branes. We will show that it leads to a generalised geometry involving an extension of our usual formulation of space-time.

This colloquium reviews old and new no go theorems that severely constrain possible interactions of massless high spin particles. Massive particles can interact with gauge fields and gravity, but often they are plagued by pathologies such as superluminal propagation in nontrivial backgrounds. The last part of the talk uses the example of open string theory to show that such pathologies can be avoided by an appropriate choice of non-minimal interactions.

We revisit the relationship between the 6D (2, 0) M5 CFT compactified on a circle to 5D maximally supersymmetric YM Gauge Theory. We show that in the broken phase 5D SYM contains a spectrum of soliton states that can be identified with the complete KK modes of an M2 ending on the M5's. This provides evidence that the (2,0) theory on a circle is equivalent to 5D SYM with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

Understanding the phases of string theory in the strong curvature and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.