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We shall discuss aspects of how internal manifolds evolve during cosmology, paying particular attention to the regions where the manifold changes topology.

I will discuss how to use string techniques to systematically derive brane world effective actions for models with magnetized (or equivalently intersecting) D-branes. In particular, I derive the dependence on all NS-NS moduli of the kinetic terms of the chiral matter in a generic non-supersymmetric brane configurations with non-commuting open string fluxes. Near a N=1 supersymmetric point the effective action contains D and F term breaking terms which can be explicitly computed with string diagrams.

We review AdS/CFT Correspondence constructions of non-supersymmetric theories and include quarks using D7 brane probes. Such geometries provide a geometric decription of chiral symmetry breaking in the pattern of QCD. The meson masses of the theory can be computed and include a pion-like goldstone boson. Phenomenological models of QCD in this spirit surprisingly work at the 10-15 percent level. Finally we address a major concern with such models - they have strongly coupled UV physics. We use ideas from perfect lattice actions to suggest a solution and show a toy example of the method in action.

We study the quantization on the torus of the N=2 spinning particle coupled to spacetime gravity to obtain a worldline representation of the effective action of an arbitrary antisymmetric tensor field. This representation contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Then we describe how to use it: (i) to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions, (ii) to derive exact duality relations, and (iii) to compute some correlation functions.

This talk will survey recently deduced features of the ten-dimensional effective action for four gravitons in type II string theories. Duality with M-theory together with supersymmetry leads to a number of nontrivial higher derivative four-graviton interactions whose non-perturbative structure is completely determined by a collection of Poisson equations on moduli space and is consistent with data provided by string perturbation theory.

I will review recent results at strong and weak coupling in N=4 SYM theory at finite temperature. I will point out that retarded correlators have a qualitatively different analytic structure in the weak a strong coupling limits and will argue that this either necessitates a phase transition in the theory or requires that we revise our current understanding of weakly coupled plasmas.